SEARCDE 2017

Thirty-Seventh Southeastern-Atlantic Regional

Conference on Differential Equations

October 7-8

searcde2017@kennesaw.edu

(470) 578-7235

Plenary Speakers

Jerry L. Bona University of Illinois at Chicago

Alfonso Castro Harvey Mudd College

Suzanne Lenhart University of Tennessee

Michael Y. Li University of Alberta

Conference Venue

Kennesaw Campus

Science Building & Clendenin Building

275 Kennesaw State University Road

Kennesaw, GA 30144

For more information, visit

http://conference.kennesaw.edu/searcde

Thirty-Seventh Southeastern-Atlantic Regional Conference

on Differential Equations

Program and Abstracts

October 7–8, 2017

Welcome!

Welcome to the 37th Southeastern-Atlantic Regional Conference on Differential Equations.

We hope you will enjoy the talks, food, great weather, and the beautiful Kennesaw State University (KSU) campus.

We would also appreciate any feedback and any suggestions you have. Please fill out the feedback form included inyour registration materials or send comments to Dhruba Adhikari (dadhikar@kennesaw.edu).

Sincerely,SEARCDE 2017 Local Organizing CommitteeDhruba Adhikari (chair)Sean EllermeyerKen KeatingLudmila Orlova-ShokryNicolae PascuLake RitterLiancheng Wang

SEARCDE Steering Committee

Dhruba Adhikari (Kennesaw State University)Folashade Agusto (University of Kansas)Lorena Bociu (North Carolina State University)John Graef (University of Tennessee at Chattanooga)Eric Numfor (Augusta University)Jaffar Ali Shahul-Hameed (Florida Gulf Coast University)

Conference Support Provided By

KSU The Office of the Vice President of ResearchKSU College of Science and MathematicsKSU Department of MathematicsAxioms — An Open Access Journal from MDPICommunications in Applied Analysis, Dynamic Publishers, Inc.KSU University Stores

Accessing KSU WiFi Network

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Location of Talks

The conference will take place in the Clendenin, Science, and Science Lab Buildings, abbreviated CL, SC, and SL,respectively. See the campus map in your registration packet for directions. Registration and all breaks will be in theClendenin and Science Lab Building Atriums (CL Atrium 1000 and SL Atrium 1001).

Campus Parking Map

On Saturday and Sunday you can park for free in the East Deck (only accessible from Frey Rd), Lot A, and the WestDeck. These areas are circled in blue on the map above. The main KSU Entrance is circled in red.All these lots are conveniently close to the Science and Clendenin Buildings. Lot A is the closest to the buildings.

Please take notice, open parking excludes dedicated parking spaces, service vehicle spaces, loading/unloading spaces,handicap spaces, fire lanes and police spaces.

Summary of the 2017 SEARCDE Program

Saturday, October 711:00am – 6:00pm Registration (CL Atrium 1000)

12:45pm – 1:00pm Opening Remarks (SC 109)Marcus Davis, Associate Dean for Research of the College of Science and MathematicsSean F. Ellermeyer, Chair of the Department of Mathematics

1:00pm – 2:00pm Suzanne Lenhart: Modeling Infectious Diseases with Environmental TransmissionPlenary 1 Moderator: Sean F. Ellermeyer (SC 109)

2:00pm – 2:20pm Coffee Break (SL Atrium 1001)PARALLEL SESSIONS

Session 1A Session 1B Session 1C Session 1D Session 1E Session 1FRoom: CL 1003 CL 1008 CL 1010 SC 212 SC 213 SC 214

Moderator: P. Laval C. Browne I. Aslan D. Ramirez C. Collins L. Ritter2:20pm – 2:40pm V. Alexiades C. Browne I. Aslan D. Ramirez C. Collins L. Ritter2:40pm – 3:00pm H. Bhatt N. Vaidya D. Burton L. Hermi M. Fury S. Rengaswami3:00pm – 3:20pm S. Liao M. Elmas C. Edholm C. Buse, L.

NguyenD. Regmi H. Kankana-

malage3:20pm – 3:40pm R. Leander H. Gulbudak E. Numfor J. Gemmer C. Lorton Z. Shuai3:40pm – 3:55pm Coffee Break (SL Atrium 1001)

PARALLEL SESSIONS

Session 2A Session 2B Session 2C Session 2D Session 2E Session 2FRoom: CL 1003 CL 1008 CL 1010 SC 212 SC 213 SC 214

Moderator: X. Gong H. Joshi M. Islam M. Wang R. Sharma S. Ngai3:55pm – 4:15pm X. Gong H. Joshi M. Islam M. Wang R. Sharma S. Ngai4:15pm – 4:35pm N. Iraniparast J. Murdock S. Almuthaybiri E. Demirci R. Mickens S. Robinson4:35pm – 4:55pm S. Ai H. Matlock Z. Denton R. Dahal M. Hameed M. Rivas4:55pm – 5:15pm M. Noorman L. Hadji Y. Raffoul T. Wohrer I. Amirali F. Drullion5:20pm – 6:20pm Michael Li: Mathematical Models for Infectious Diseases with Nonlocal State Structures

Plenary 2 Moderator: Liancheng Wang (SC 109)

6:30pm – 8:30pm RECEPTION DINNER (University Room A, B, C)

Sunday, October 87:30am – 11:00am Registration (CL Atrium 1000)7:30am – 8:30am Light Breakfast and Coffee (SL Atrium 1001)8:30am – 9:30am Alfonso Castro: Critical Point Theory and Multiplicity of Solutions to Elliptic Boundary Value Problems

Plenary 3 Moderator: Dhruba Adhikari (SC 109)9:30am – 9:50am Coffee Break (SL Atrium 1001)

PARALLEL SESSIONS

Session 3A Session 3B Session 3C Session 3D Session 3E Session 3FRoom: CL 1003 CL 1008 CL 1010 SC 212 SC 213 SC 214

Moderator: Y. Shao Z. Sinkala Y. Chung L. Castle L. Kong S. Sadhu9:50am – 10:10am Y. Shao Z. Sinkala Y. Chung L. Castle L. Kong S. Sadhu10:10am – 10:30am S. Subedi K. Poudel B. Pineyro K. Sonnanburg J. Neugebauer D. Wanduku10:30am – 10:50am J. Navratil A. Olifer Q. Chen Y. Zeng D. Maroncelli J. Graef10:50am – 11:10am D. Guo O. Egbelowo J. Paullet S. Ravindran A. Ludu M. Lafcı11:10am – 11:30am Coffee Break (SL Atrium 1001)11:30am – 12:30pm Jerry L. Bona: Applications of Water Wave Theory in Oceanography and Coastal Engineering

Plenary 4 Moderator: John Graef (SC 109)12:30pm – 1:30pm Lunch (SL Atrium 1001)

PARALLEL SESSIONS

Session 4A Session 4B Session 4C Session 4D Session 4ERoom: CL 1003 CL 1008 CL 1010 SC 212 SC 213

Moderator: W. Ding K. Berry B. Pantha K. Acharya C. Kunkel1:30pm – 1:50pm W. Ding K. Berry B. Pantha K. Acharya C. Kunkel1:50pm – 2:10pm L. Corsi J. Zanussi T. Miyaoka E. Harrell II D. Benko2:10pm – 2:30pm A. FALADE W. Valega-

MackenzieY. Dib Y. Hu C. Okhio, L.

Crimm2:30pm – 2:50pm D. Mathebula J. Nanware S. Sarwar Z. Allali

2:50pm Closing Remarks (SC 109), Coffee Available (SL Atrium 1001)

Thirty-Seventh Southeastern-Atlantic Regional Conferenceon Differential Equations

Kennesaw State University, Georgia

ProgramSaturday, October 7

11:00am – 6:00pm Registration (CL Atrium 1000)12:45pm – 12:55pm Conference Opening (Room: SC 109)

Opening - Dhruba AdhikariWelcome - Marcus Davis, Associate Dean for Research of the College of Science and MathematicsRemarks - Sean F. Ellermeyer, Chair of the Department of Mathematics

1:00pm – 2:00pm Plenary 1 (Room: SC 109)Modeling Infectious Diseases with Environmental TransmissionSuzanne Lenhart, University of Tennessee, Knoxville

2:00pm – 2:20pm Coffee Break (SL Atrium 1001)

Parallel Sessions 1A – 1F

Session 1A (Room: CL 1003)2:20pm – 2:40pm Vasilios Alexiades Band formation in bacterial aerotaxis2:40pm – 3:00pm Harish Bhatt Efficient Krylov Exponential Time Differencing Method for 3D

Advection-Diffusion-Reaction Systems3:00pm – 3:20pm Shasha Liao Nonlinear Modulational Instability of Dispersive PDE Models3:20pm – 3:40pm Rachel Leander Drift-diffusion threshold models for the analysis of cellular decisions

Session 1B (Room: CL 1008)2:20pm – 2:40pm Cameron Browne Dynamics of Virus and Immune Response Network Models2:40pm – 3:00pm Naveen K. Vaidya Modeling Pharmacodynamics on HIV Latent Infection3:00pm – 3:20pm Mustafa Elmas A two pathways model for chemotactic signaling in Azospirillum brasilense3:20pm – 3:40pm Hayriye Gulbudak Modeling Distinct Virus Infection Strategies in Virus-Microbe Systems

Session 1C (Room: CL 1010)2:20pm – 2:40pm Ibrahim Aslan Vaccine Impulse Model of Leptospirosis in Cattle2:40pm – 3:00pm Danielle Burton Harvest timing in difference equations3:00pm – 3:20pm Christina Edholm A Risk Structured Mathematical Model of Buruli Ulcer Disease in Ghana3:20pm – 3:40pm Eric Numfor Management Strategies in a Malaria Model Combining Human

and Transmission-blocking Vaccines

Session 1D (Room: SC 212)2:20pm – 2:40pm Diego Ramirez Monotone Method for Caputo Fractional Differential Equations with Impulses2:40pm – 3:00pm Lotfi Hermi On improving isoperimetric inequalities for the fundamental tone

of a vibrating membrane3:00pm – 3:20pm C. Buse, L. Nguyen Asymptotic stability for individual trajectories of discrete periodic

evolution families of operators in Banach spaces3:20pm – 3:40pm John Gemmer Least Action Methods and Noise Induced Transitions in Periodically

Forced Systems

Session 1E (Room: SC 213)2:20pm – 2:40pm Craig D. Collins Two-level Schwarz Methods for Discontinuous Galerkin Approximations

of Second Order Elliptic Problems2:40pm – 3:00pm Matthew Fury Logarithmic, well-posed approximation of the backward heat equation

in Lp spaces, p in (1,∞)3:00pm – 3:20pm Dipendra Regmi Global weak solution of magnetohydrodynamic equations with

partial dissipation and diffusion3:20pm – 3:40pm Cody Lorton An Efficient Numerical Method for Electromagnetic Scattering in Random Media

Session 1F (Room: SC 214)2:20pm – 2:40pm Lake Ritter A delay differential equation model of activation of endothelial

nitric oxide synthase2:40pm – 3:00pm Sathyanarayanan Rengaswami Existence and Uniqueness of Solutions

to Infinite Dimensional Kuramoto Model3:00pm – 3:20pm Hasala Senpathy Gallolu Kankanamalage Two type Lyapunov-Krasovskii Characterizations

of Input-to-Output Stability for Systems with Delays3:20pm – 3:40pm Zhisheng Shuai A Graph-Theoretic Approach to the Construction of Lyapunov Functions

3:40pm – 3:55pm Coffee Break (SL Atrium 1001)

Parallel Sessions 2A – 2F

Session 2A (Room: CL 1003)3:55pm – 4:15pm Xiaoqian Gong Existence and Uniqueness of Measure Valued Solutions to a Hyperbolic

Conservation Law with In-flux and Out-flux4:15pm – 4:35pm Nezam Iraniparast Solutions to a First Order Hyperbolic System4:35pm – 4:55pm Shangbing Ai Travelling wave solutions for nonlocal predator-prey models4:55pm – 5:15pm Marcella Noorman Local Sensitivity Analysis for 1D Poro-Elastic and Poro-Visco-Elastic Models

Session 2B (Room: CL 1008)3:55pm – 4:15pm Hem Joshi Modeling Agal Blooms4:15pm – 4:35pm J. Angela Hart Murdock Seasonal Effects on Sources and Large Mouth Bass Predation

in Normandy Lake4:35pm – 4:55pm Hugh Matlock Modeling different protocols of dendritic cell therapy for melanoma4:55pm – 5:15pm Layachi Hadji Mathematical modeling of nonlinear convection induced by the sequestration

of carbon dioxide in a geological formation

Session 2C (Room: CL 1010)3:55pm – 4:15pm Muhammad Islam Bounded Solutions of a Volterra integrodifferential equation4:15pm – 4:35pm Saleh S. Almuthaybiri Quasilinearization and Boundary Value Problems at Resonance

for Caputo Fractional Differential Equations4:35pm – 4:55pm Zachary Denton Monotone method for systems of RL fractional inegro-differential equations4:55pm – 5:15pm Youssef Raffoul Discretization scheme in Volterra integro-differential equations

that preserves stability and boundedness

Session 2D (Room: SC 212)3:55pm – 4:15pm Min Wang Existence of solutions for a nonlocal fractional boundary value problem4:15pm – 4:35pm Elif Demirci A Fractional Order Epidemic Model for HBV in a Non-Constant Population4:35pm – 4:55pm Rajendra Dahal New monotonicity conditions in discrete fractional calculus with applications

to extremality conditions4:55pm – 5:15pm Tobias Wohrer Large time behavior in defective Fokker-Planck equations

Session 2E (Room: SC 213)3:55pm – 4:15pm Ramjee Sharma On the numerical solutions of 2D Boussinesq equations with fractional dissipation4:15pm – 4:35pm Ronald E. Mickens Approximate Solution to the ODE modeling thermal expulsion

of fluid from a slender heated tube4:35pm – 4:55pm Muhammad Hameed Mathematical Modeling of the Breakup of a Slender Fluid Jet

with Variable Surface Tension4:55pm – 5:15pm Ilhame Amirali Numerical Solution of Parameterized Singularly Perturbed Problem

with Integral Boundary Condition

Session 2F (Room: SC 214)3:55pm – 4:15pm Sze-Man Ngai Spectral asymptotics of some one-dimensional fractal Laplacians4:15pm – 4:35pm Stephen Robinson Characterizing the Fucik Spectrum for the p−Laplacian4:35pm – 4:55pm Mauricio Rivas Eigencurves for the two-parameter Robin-Steklov eigenproblem for the Laplacian4:55pm – 5:15pm Frederique Drullion Growth of groups of wind generated waves

5:20pm – 6:20pm Plenary 2 (Room: SC 109)Mathematical Models for Infectious Diseases with Nonlocal State StructuresMichael Li, University of Alberta

6:30pm – 8:30pm RECEPTION DINNER (University Rooms A, B, C)

Sunday, October 8

7:30am – 11:00am Registration (CL Atrium 1000)7:30am – 8:30am Coffee (SL Atrium 1001)

8:30am – 9:30am Plenary 3 (SC 109)Critical Point Theory and Multiplicity of Solutions to Elliptic Boundary Value ProblemsAlfonso Castro, Harvey Mudd College

9:30am – 9:50am Coffee Break (SL Atrium 1001)

Parallel Sessions 3A – 3F

Session 3A (Room: CL 1003)9:50am – 10:10am Yuanzhen Shao Wellposedness of a Nonlocal Nonlinear Diffusion Equation of Image Processing10:10am – 10:30am Subhash Subedi Blow-up problem for one dimensional fractional reaction diffusion equation10:30am – 10:50am Josef Navratil Stationary solutions of reaction-diffusion equations with unilateral regulations10:50am – 11:10am Daniel Guo Numerical Solutions of Time-Dependent Partial Differential Equation

Session 3B (Room: CL 1008)9:50am – 10:10am Zachariah Sinkala A dynamical system model of a locally advanced non-small cell lung cancer

with chemo-radiotherapy10:10am – 10:30am Khem Poudel Modeling T cell proliferation in response to lung cancer in mice10:30am – 10:50am Andrei Olifer A model of a virtual community with a decentralized reputation-based

peer evaluation10:50am – 11:10am Oluwaseun F Egbelowo Application of nonstandard finite difference method to three

compartment pharmacokinietics models

Session 3C (Room: CL 1010)9:50am – 10:10am Yu-Min Chung Inertial Manifolds Computations10:10am – 10:30am Benedict Pineyro Super Time-Stepping Schemes for Conduction-Radiation

Heat Transfer Problem10:30am – 10:50am Qingshan Chen The barotropic quasi-geostrophic equation under a free surface10:50am – 11:10am Joseph Paullet Analysis of Stagnation Point Flow of an Upper-Convected Maxwell Fluid

Session 3D (Room: SC 212)9:50am – 10:10am Lucas Castle Well-Posedness and Control in a Free Boundary Fluid-Structure Interaction10:10am – 10:30am Kevin Sonnanburg Blow-up Continuity in Mean Curvature Flow10:30am – 10:50am Yanni Zeng Lp Asymptotic Behavior of Solutions to General Hyperbolic-Parabolic

Systems of Balance Laws in Multi Space Dimensions10:50am – 11:10am S. S. Ravindran Dirichlet Control Using Boundary Penalty Method for Unsteady

Navier-Stokes Equations

Session 3E (Room: SC 213)9:50am – 10:10am Lingju Kong On a discrete fourth order boundary value problem10:10am – 10:30am Jeffrey Neugebauer Solutions of Boundary Value Problems at Resonance with Periodic

and Antiperiodic Boundary Conditions

10:30am – 10:50am Dan Maroncelli Nonlinear Sturm-Liouville problems with nonlocal boundary conditions10:50am – 11:10am Andrei Ludu Differential Equations of Dynamical Order

Session 3F (Room: SC 214)9:50am – 10:10am Susmita Sadhu Noise induced mixed-mode oscillations in a stochastic predator-prey

system with two time-scales10:10am – 10:30am Divine Wanduku The fundamental properties of a family of stochastic epidemic dynamic

models for vector-borne diseases. Case study: malaria10:30am – 10:50am John Graef Some existence results for systems of second-order impulsive differential equations10:50am – 11:10am Mehtap Lafcı On Periodicity of Solutions of an Impulsive Differential Equation

with Piecewise Constant Arguments

11:10am – 11:30am Coffee Break (SL Atrium 1001)

11:30am – 12:30pm Plenary 4 (Room: SC 109)Applications of Water Wave Theory in Oceanography and Coastal EngineeringJerry L. Bona, University of Illinois at Chicago

12:30pm – 1:30pm Lunch (SL Atrium 1001)

Parallel Sessions 4A – 4E

Session 4A (Room: CL 1003)1:30pm – 1:50pm Wandi Ding Mathematical Models of Community-acquired and Hospital-acquired

Methicillin-resistant Staphylococcus Aureus (MRSA) transmissionin Hospital and Community Settings

1:50pm – 2:10pm Livia Corsi Quasi-periodic solutions for dispersive PDEs2:10pm – 2:30pm Abdulahi Falade Mathematical modelling of within-host dynamics of cholera: bacterial

viral interaction2:30pm – 2:50pm Dephney Mathebula Mathematical Modelling vector-borne diseases

Session 4B (Room: CL 1008)1:30pm – 1:50pm Kileen Berry An Energy-Based Blending of Classical Elasticity and Peridynamics1:50pm – 2:10pm Jacy Zanussi Is Allee Effect critical for tumor progression?2:10pm – 2:30pm Wencel Valega-Mackenzie Modeling The Impact of Zika Virus Epidemic with Vaccination2:30pm – 2:50pm Jagdish A. Nanware Monotone Method for Finite System of Riemann-Liouville Sequential

Fractional Differential Equations with Periodic Boundary Conditions

Session 4C (Room: CL 1010)1:30pm – 1:50pm Buddhi Pantha Optimal control applied to a spatio-temporal anthrax Model1:50pm – 2:10pm Tiago Miyaoka Optimal control of vaccination in a PDE model for Zika virus2:10pm – 2:30pm Youssef Dib Optimization of Cash Management Fluctuation2:30pm – 2:50pm Shahzad Sarwar Dynamics of Fractional Differential Systems with Riemann-Liouville

and Hadamard Derivatives

Session 4D (Room: SC 212)1:30pm – 1:50pm Keshav Acharya Titchmarsh-Weyl theory for vector valued discrete Schrodinger operators1:50pm – 2:10pm Evans M. Harrell II Localization of eigenfunctions on quantum graphs2:10pm – 2:30pm Yi Hu Blowup rate for rotational nonlinear Schroedinger equations2:30pm – 2:50pm Zakaria El Allali Eigenvalue problems for p(x)–Kirchho-type equations

with Neumann boundary conditions

Session 4E (Room: SC 213)1:30pm – 1:50pm Curtis Kunkel A Summer Undergraduate Research Project in Fractional

Difference Equations1:50pm – 2:10pm David Benko Energy estimation of long distance runners2:10pm – 2:30pm C. Okhio, L. Crimm Experimental and Numerical Investigation of a Flow-Leak Simulator2:30pm – 2:50pm

2:50pm Closing Remarks (Room: SC 109), Coffee Available in SL Atrium 1001

Biographies of Plenary Speakers

Jerry L. Bona: Jerry L. Bona is a Professor of Mathe-matics at the University of Illinois at Chicago. He receivedhis Ph.D. from Harvard University under supervision of GarrettBirkhoff. He worked from 1970 to 1972 at the Fluid Me-chanics Research Institute University of Essex, where along withBrooke Benjamin and J. J. Mahony, he published the paper“Model Equations for Long Waves in Nonlinear Dispersive Sys-tems”, where Benjamin-Bona-Mahony (BBM) equation was firststudied in detail. Professor Bona has also worked at Uni-versity of Chicago, Pennsylvania State University and Univer-sity of Texas at Austin. In 2012, he became a fellow ofthe American Mathematical Society. In 2013, he became afellow of the Society for Industrial and Applied Mathematics.

Alfonso Castro: Alfonso Castro is a Professor of Mathematics at HarveyMudd College. He got his Ph.D. degree at the University of Cincinnati un-der the advisorship of Professor Alan C. Lazer. His recent work is con-centrated on semilinear equations. Professor Castro is a world renowned ex-pert in the area of Partial Differential Equations. In particular, his interestlies in variational methods, inverse problems and water waves (solitons). Hehas more than forty coauthors. He served as the program director of Na-tional Science Foundation from 1989 to 1991. He is in the editorial boardof many journals. Most notably, he is the Co-founder and Managing Edi-tor of the open access journal – Electronic Journal of Differential Equations.

Suzanne Lenhart: Suzanne Lenhart is a Chancellor’s Professor and the James R. Cox Professor of Mathematicsat the University of Tennessee, Knoxville, and is the Associate Director for Education and Outreach at the NationalInstitute for Mathematical and Biological Synthesis (NIMBioS, funded by the National Science Foundation). She iscurrently also a member of the UT Center for Wildlife Health. She was a part-time member of the research staff atOak Ridge National Laboratory for 22 years.

Professor Lenhart is an applied mathematician working in partial differ-ential equations, ordinary differential equations and optimal control. Hercurrent research focuses on population models with applications in infec-tious diseases, invasive species, and natural resources. She has authoredmore than 180 journal articles, as well as 3 books, including Optimal Con-trol Applied to Biological Models and Mathematics for the Life Sciences.She is a fellow of the American Mathematical Society, the American Asso-ciation for the Advancement of Science and SIAM.

Professor Lenhart has extensive education and outreach experience. Shedirected the Research Experiences for Undergraduates program in the De-partment of Mathematics for 15 years and now directs such a program atNIMBioS since 2009. She was President of the Association for Women inMathematics (AWM) in 2001-2003. She has worked with the Bearden HighSchool Math Club since 2002.

Michael Li: Michael Li is a Professor of Mathematics at the University of Alberta.He received his Ph.D. from the University of Albert and then did postdoctoral workat the Center for Dynamical Systems and Nonlinear Analysis at Georgia Tech. Beforereturning to Canada, he held academic positions at Mississippi State University.

Professor Michael Li’s research focuses on global dynamics of high dimensional sys-tems of differential equations, with applications to mathematical epidemiology andmathematical modeling of viral dynamics. His research has been funded by the Na-tional Science Foundation (NSF), Natural Sciences and Engineering Research Councilof Canada (NSERC), and Canada Foundation for Innovation (CFI).

Plenary Talks

1. Title: Applications of Water Wave Theory in Oceanography and Coastal EngineeringSpeaker: Jerry L. BonaInstitution: The University of Illinois at ChicagoEmail: bona@math.uic.edu

Abstract: After a review of salient parts of surface water wave theory and some indication of recent rigorousresults pertaining to it, the lecture will turn to some applications of these theories. This will include tsunamipropagation, rogue wave formation, beach protection strategy and pulmonary hypertension, as time allows.

2. Title: Critical Point Theory and Multiplicity of Solutions to Elliptic Boundary Value ProblemsSpeaker: Alfonso CastroInstitution: Harvey Mudd CollegeEmail: castro@g.hmc.edu

Abstract: We will review critical point theory techniques and combine them to establish the existence ofmultiple solutions to boundary value problems of the form ∆u+ g(u) = 0 in Ω and u = 0 on the boundary of Ω,where Ω is a smooth bounded region in RN . In particular, sufficient conditions for this problem to have sevensolutions for g sublinear in the absence of symmetries will be discussed.

3. Title: Modeling Infectious Diseases with Environmental TransmissionSpeaker: Suzanne LenhartInstitution: The University of Tennessee, KnoxvilleEmail: lenhart@math.utk.edu

Abstract: Modeling infectious diseases that have an indirect transmission route through pathogens in theenvironment is a research area with growing interest. Whether to use this approach may depend on how longthe pathogen stays viable in the environment. The appropriate types of transmission terms to include may varydepending on the disease. Examples of models representing Johne’s Disease in dairy cattle and ClostridiumDifficile in hospital-acquired infections will be discussed.

4. Title: Mathematical Models for Infectious Diseases with Nonlocal State StructuresSpeaker: Michael LiInstitution: University of Alberta, CanadaEmail: mli@math.ualberta.ca

Abstract: In this talk, I will discuss state structures in mathematical models for infectious diseases. The stateis a measure of infectivity of an infected individual in epidemic models or the intensity of viral replications in aninfected cell for in-host models. In modelling, a state structure can be either discrete or continuous.

In a discrete state structure, a model is described by a large system of coupled ODEs. The complexity ofthe system often poses a serious challenge for the analysis of the system dynamics. I will show how such acomplex system can be viewed as a dynamical system defined on a transmission-transfer network (digraph), andhow a graph-theoretic approach to Lyapunov functions developed by Guo-Li-Shuai can be applied to rigorouslyestablish the global dynamics.

In a continuous state structure, the model gives rise to a system of nonlinear integro-differential equations witha nonlocal term. The mathematical challenges for such a system include a lack of compactness of the associatednonlinear semigroup. The well-posedness and dissipativity of the semigroup is established by directly verifyingthe asymptotic smoothness. An equivalent principal spectral condition between the next-generation operatorand the linearized operator allows us to link the basic reproduction number R0 to a threshold condition for thestability of the disease-free equilibrium. The proof of the global stability of the endemic equilibrium utilizes aLyapunov function whose construction is informed by the graph-theoretic approach in the discrete case.

Contributed Talks

1. Title: Titchmarsh-Weyl theory for vector valued discrete Schrodinger operatorsSpeaker: Keshav AcharyaInstitution: Embry-Riddle Aeronautical UniversityEmail: acharyak@erau.edu

Abstract: We discuss the basic theory of Weyl m function for vector valued discrete Schrodinger operators.This is an extension of the theory from one dimensional space.

2. Title: Travelling wave solutions for nonlocal predator-prey modelsSpeaker: Shangbing AiInstitution: University of Alabama in HuntsvilleEmail: ais@uah.eduCo-author(s): Yihong Du (Univ. of New England, Australia), Rui Peng (Jiangsu Normal Univ., China)

Abstract: We study the existence of traveling wave solutions (u(x + ct), v(x + ct)) for time-delayed and/orspatial-nonlocal predator-prey models. These traveling wave solutions connect the prey-only equilibrium (K, 0)at x = −∞ and the co-existence equilibrium (u∗, v∗) at x =∞. We first obtain a result on the existence of weaktraveling wave solutions for a general class of nonlocal predator-prey models for every wave speed c bigger thanor equal to the minimal speed; these solutions are not required to satisfy the boundary condition at x = ∞.We then apply this result to some particular models to obtain their weak traveling wave solution; with someadditional conditions, we show that these weak traveling wave solutions are traveling wave solutions of thesemodels.

3. Title: Eigenvalue problems for p(x)−Kirchhoff-type equations with Neumann boundary conditionsSpeaker: Zakaria El AllaliInstitution: Georgia Institute of TechnologyEmail: elallali@hotmail.com

Abstract: This work is concerned with the existence of nontrivial weak solutions for a p(x)−Kirchhoff-typeequation with Neumann boundary conditions. By using the Mountain Pass Theorem of Ambrosetti and Ra-binowitz, Ekelands variational principle and the theory of the variable exponent Sobolev spaces, we establishconditions for the existence of weak solutions.

4. Title: Band formation in bacterial aerotaxisSpeaker: Vasilios AlexiadesInstitution: University of Tennessee, KnoxvilleEmail: alexiades@utk.eduCo-author(s): Mustafa Elmas, Gladys Alexandre

Abstract: Azospirillum brasilense are micro-aerophilic soil bacteria. They live at roots of many cereals andgrasses, promoting plant growth by fixing nitrogen under low oxygen conditions. They preferentially concentratewhere oxygen concentration is most favorable to them. In experiments, they form ”bands” that become visible.We study a model of bacterial aerotaxis which consists of a system of diffusion-reaction and advection-reactionPDEs describing diffusion of oxygen in water and chemotactic movement of bacteria. We present simulationsthat show the effect of some of the parameters on the formation of the band.

5. Title: Quasilinearization and Boundary Value Problems at Resonance for Caputo Fractional Differential Equa-tions.Speaker: Saleh S. AlmuthaybiriInstitution: University of DaytonEmail: almuthaybiris1@udayton.eduCo-author(s): Paul Eloe

Abstract: The quasilinearization method is applied to a boundary value problem at resonance for a Caputofractional differential equation. The method of upper and lower solutions is first employed to obtain the unique-ness of solutions of the boundary value problem at resonance. The shift method is applied to show the existence

of solutions. The quasilinearization algorithm is then developed and sequences of approximate solutions are con-structed that converge monotonically and quadratically to the unique solution of the boundary value problemat resonance.

6. Title: Numerical Solution of Parameterized Singularly Perturbed Problem with Integral Boundary ConditionSpeaker: Ilhame AmiraliInstitution: Duzce UniversityEmail: ailhame@gmail.comCo-author(s): Gabil M. Amiraliyev, Mustafa Kudu

Abstract: In this presentation, parameter-uniform numerical method for a parameterized singularly perturbedordinary differential equation containing integral boundary condition is studied. Asymptotic estimates on thesolution and its derivatives are derived. A numerical algorithm based on upwind nite difference operator andappropriate piecewise uniform mesh is constructed. Parameter-uniform error estimate for the numerical solutionis established. Numerical results are presented, which illustrate the theoretical results.

7. Title: Vaccine Impulse Model of Leptospirosis in CattleSpeaker: Ibrahim AslanInstitution: University of Tennessee, KnoxvilleEmail: iaslan@vols.utk.eduCo-author(s): Suzanne Lenhart, David Baca

Abstract: As one of the most widespread zoonotic disease, Leptospirosis became endemic particularly intropical and subtropical regions where the environment provides favorable conditions for propagation of thedisease. It causes large economic loss in livestock industry. In this talk, we introduce a SVIR dynamical systemof ordinary differential equations with impulse action of vaccination at certain times in order to investigatewhether the disease can be controlled with current vaccine schedules. Some analytical and numerical results willbe presented.

8. Title: Energy estimation of long distance runnersSpeaker: David BenkoInstitution: University of South AlabamaEmail: dbenko@southalabama.edu

Abstract: Long distance runners speed up towards the end of the race. We try to come up with an explanationas well as come up with a method how they can (theoretically) estimate their energy.

9. Title: An Energy-Based Blending of Classical Elasticity and PeridynamicsSpeaker: Kileen BerryInstitution: University of Tennessee, KnoxvilleEmail: kberry11@vols.utk.eduCo-author(s): Steven Wise, Tadele Mengesha

Abstract: Classically, material deformations are modeled using partial differential equations. Classical Elastic-ity is a local model that requires the assumption that the material deformation has some degree of smoothness.Alternatively, Peridynamics is an integral based nonlocal reformation of continuum mechanics. This modeleliminates the use of special derivatives by allowing particles to interact over a finite distance. Thus, Peridy-namics is effective in representing discontinuous deformations, but due to the use of integration rather thandifferentiation, it is more computationally expensive. By modeling the region where discontinuous deformationis suspected with Peridynamics and by modeling away from that region with Classical Elasticity, the negativeaspects of both models can be diminished. As many material scientists and engineers look at the energy of thesystem in order to study the deformation, it is natural to blend these two methods at the energy level. Thewell-posedness of this model is established using variational methods and its development follows the analysis ofthe purely peridynamic model.

10. Title: Efficient Krylov Exponential Time Differencing Method for 3D Advection-Diffusion-Reaction SystemsSpeaker: Harish BhattInstitution: Savannah State UniversityEmail: harishbht24@gmail.com

Abstract: The number of ordinary differential equations generally increases exponentially as the partial dif-ferential equation is posed on a domain with more dimensions. This is, of course, the curse of dimensionality forexponential time differencing methods. The computational challenge in applying exponential time differencingmethods for solving partial differential equations in high spatial dimensions is how to compute the matrix expo-nential functions for very large matrices accurately and efficiently. In this talk, we will present efficient Krylovsubspace approximation-based locally extrapolated exponential time differencing method for solving a three-dimensional nonlinear advection-diffusion-reaction system. In addition, we will illustrate the performance andreliability the method by testing it on systems of the three-dimensional nonlinear advection-diffusion-reactionequations and three-dimensional viscous nonlinear Burgers’ equation.

11. Title: Dynamics of Virus and Immune Response Network ModelsSpeaker: Cameron BrowneInstitution: University of Louisiana at LafayetteEmail: cambrowne@louisiana.edu

Abstract: The dynamics of virus and immune response within a host can be viewed as a complex and evolvingecological system. For example, during HIV infection, an array of CTL immune response populations recognizespecific epitopes (viral proteins) presented on the surface of infected cells to effectively mediate their killing.However HIV can rapidly evolve resistance to CTL attack at different epitopes, inducing a dynamic networkof viral and immune response variants. We consider models for the network of virus and immune responsepopulations, consisting of Lotka-Volterra-like systems of ordinary differential equations. Stability of severalequilibria and uniform persistence of distinct viral/immune variants are characterized utilizing a Lyapunovfunction. Our analysis provides insights on viral immune escape from multiple epitopes. In the “binary mutation”setting, we prove that if the viral fitness costs for gaining resistance to each epitope are equal, then the systemof 2n virus strains converges to a “perfectly nested network” with less than or equal to n + 1 persistent virusstrains. Overall, our results suggest that immunodominance, i.e. relative strength of immune response to anepitope, is the most important factor determining the persistent network structure.

12. Title: Harvest timing in difference equationsSpeaker: Danielle BurtonInstitution: University of Tennessee, KnoxvilleEmail: dburton3@vols.utk.eduCo-author(s): Suzanne Lenhart, University of Tennessee; Frank Hilker, University of Osnabruck; DanielFranco, Universidad Nacional de Educacion a Distancia

Abstract: Management decisions regarding harvest are complicated and difficult. In the difference equationsetting, order of events cases have been studied. Hiromi Seno proposed a model to study the timing of harvestbetween breeding seasons by taking a convex combination of the order of events cases reproduce-harvest andharvest-reproduce. We derive new models that mechanistically incorporate harvest timing and share somepreliminary results.

13. Title: Asymptotic stability for individual trajectories of discrete periodic evolution families of operators inBanach spacesSpeaker: Constantine Buse and Lan NguyenInstitution: Western Kentucky UniversityEmail: constantine.buse@wku.edu, lan.nguyen@wku.edu

Abstract: It is well known that a bounded linear operator T that acts on a complex Banach space X isuniformly exponentially stable (that is, its spectral radius is less than 1) if and only if for each vector b of Xand each real number µ ∈ R the solution of the following discrete Cauchy Problem

un+1 = A un + eiµnb, n ∈ Z+, µ ∈ Ru0 = 0

is bounded. We state an individual result of this type. Extensions for the case of time varying and periodiccoeffcients are also established. In the latter case, the boundedness of solutions of corresponding problem mustto be uniformly with respect to the real parameter µ.

14. Title: Well-Posedness and Control in a Free Boundary Fluid-Structure InteractionSpeaker: Lucas CastleInstitution: North Carolina State UniversityEmail: lcastle@ncsu.eduCo-author(s): Lorena Bociu, Irena Lasiecka

Abstract: We consider a system of partial differential equations modeling motion of an elastic solid inside of anincompressible fluid with a force applied to the body of the system. The fluid is modeled by the incompressibleNavier-Stokes equations while the structure is given by a damped linear wave equation. Given sufficientlyregular initial data, we establish global well-posedness in time and consider an optimal control for the problemof minimizing turbulence in the fluid flow. We establish the existence of an optimal control and discuss thederivation of the first order necessary optimality conditions that characterize the control.

15. Title: The barotropic quasi-geostrophic equation under a free surfaceSpeaker: Qingshan ChenInstitution: Clemson UniversityEmail: qsc@clemson.edu

Abstract: When the length scale of the flow is on the same order of the Rossby deformation radius, theclassical rigid-lid assumption is no longer valid, the impact of the free surface deformation on the the vorticityfield is no longer negligible, and therefore it has to be accounted for in the model. In this talk, we present somenew results concerning the well-posedness of the barotropic quasi-geostrophic equation under a free surface. Itwill be shown that, when the free surface is included as a component of the potential vorticity, the barotropicQG equation under a free surface remains globally well-posed, under certain generic assumptions on the initialstate and the boundary of the domain.

16. Title: Inertial Manifolds ComputationsSpeaker: Yu-Min ChungInstitution: University of North Carolina at GreensboroEmail: y chung2@uncg.edu

Abstract: An inertial manifold, first introduced by Foias, Sell, and Temam in 1988, is a finite-dimensional,exponentially attracting, and positively invariant Lipschitz manifold. If a dynamical system possess an inertialmanifold, it is known that all long time behaviors, such as fixed points, limit cycles, and more importantly,the global attractor, are contained in the inertial manifold. Moreover, when restricted dynamics on the inertialmanifold, such system not only becomes finite dimensional but also shares the same long time behavior of theoriginal system. Although its theory is well developed, the computation remains a challenge problem. In thistalk, we present recent progress on inertial manifolds computations, including algorithms, convergent analysis,implementations, and some open questions.

17. Title: Two-level Schwarz Methods for Discontinuous Galerkin Approximations of Second Order Elliptic Prob-lemsSpeaker: Craig D. CollinsInstitution: Murray State UniversityEmail: ccollins@murraystate.eduCo-author(s): Ohannes Karakashian, University of Tennessee, Knoxville

Abstract: The focus of this talk is to present some two-level non-overlapping and overlapping additive Schwarzmethods for solving second order elliptic problems. It is shown that the condition numbers of the preconditionedsystems are of the order O(H/h) for the non-overlapping Schwarz methods, and of the order O(H/δ) for theoverlapping Schwarz methods, where h and H represent the fine mesh size and the coarse mesh size (respectively)and δ denotes the size of the overlaps between subdomains. Numerical experiments are provided to gauge theefficiency of the methods and to validate the theory.

18. Title: Quasi-periodic solutions for dispersive PDEsSpeaker: Livia CorsiInstitution: Georgia Institute of TechnologyEmail: lcorsi6@math.gatech.eduCo-author(s): R. Feola, M. Procesi

Abstract: Given a dynamical system (in finite or infinite dimension) it is very natural to look for finitedimensional invariant subspaces on which the dynamics simplifies. Of particular interest are the invariant torion which the dynamics is conjugated to a linear one. The problem of persistence under perturbations of suchobjects has been widely studied starting form the 50’s, and this gives rise to the celebrated KAM theory. Theaim of this talk is to present an abstract result on the existence of such invariant tori, with applications to fullynonlinear dispersive PDEs.

19. Title: New monotonicity conditions in discrete fractional calculus with applications to extremality conditionsSpeaker: Rajendra DahalInstitution: Coastal Carolina UniversityEmail: rdahal@coastal.eduCo-author(s): Stanley Drvol, Christopher Goodrich

Abstract: We present some initial results for detecting extrema of a function f : Na → R when the only apriori information is some limited pointwise data about f as well as information about an appropriate fractionaldifference of f . In particular, such results provide some analogues of the well-known tests for detecting localextrema using the sign of ∆f(t). Certain of these results are consequences of some new monotonicity conditions,which relate conditions on the sign of ∆ν

af(t), for 0 < ν < 1, to the monotonicity of f . Finally, we provide somenumerical examples to illustrate the results.

20. Title: A Fractional Order Epidemic Model for HBV in a Non-constant PopulationSpeaker: Elif DemirciInstitution: Ankara University, TurkeyEmail: edemirci@ankara.edu.tr

Abstract: In this talk we develop an epidemic model including vertical transmission and vaccination to un-derstand the spread of HBV. The model we introduce is a fractional order model. We give the local stabilityanalysis of this model and obtain the basic reproduction number, R0. Finally, we give a numerical example tovalidate our mathematical results and also to clarify the reason of using fractional derivative.

21. Title: Monotone method for systems of RL fractional inegro-differential equationsSpeaker: Zachary DentonInstitution: NC A&T State UniversityEmail: zdenton@ncat.eduCo-author(s): J. D. Ramirez

Abstract: In this paper we develop the monotone method for nonlinear finite N -systems of Riemann-Liouvilleintegro-differential equations of order 0 < q < 1. The iterative technique approximates maximal and minimalcoupled quasisolutions to the nonlinear system using sequences of linear systems that are constructed via couplelower and upper solutions of varying types. Preliminary existence and comparison theorems are presented andproven where appropriate. Finally, we present a numerical example.

22. Title: Optimization of Cash Management FluctuationSpeaker: Youssef DibInstitution: University of Balamand, Koura, LebanonEmail: youssef.dib@balamand.edu.lbCo-author(s): H. Greige, Y. Raffoul, N. Kmeid

Abstract: A probabilistic model for cash management is proposed. Stochastic dynamical system is employed tostudy probability for optimum outcome. Both first step analysis and long term behavior are studied. Differenceequations are used to determine outcome. Then a study for maximizing the probability leading to maximumpossible fortune is provided.

23. Title: Mathematical Models of Community-acquired and Hospital-acquired Methicillin-resistant StaphylococcusAureus (MRSA) transmission in Hospital and Community SettingsSpeaker: Wandi DingInstitution: Middle Tennessee State UniversityEmail: wding@mtsu.eduCo-author(s): Glenn Webb, Fola B. Agusto, Ryan Florida

Abstract: Optimal control methods are applied to two deterministic mathematical models to investigate:

Model 1: To characterize the factors contributing to the replacement of hospital-acquired methicillin-resistantStaphylococcus aureus (HA-MRSA) with community-acquired methicillin-resistant Staphylococcus aureus (CA-MRSA), and quantify the effectiveness of three interventions aimed at limiting the spread of CA-MRSA inhealthcare settings. Characterizations of the optimal control strategies are established, and numerical simulationsare provided to illustrate the results.

Model 2: To investigate MRSA spread and control in a community setting.

24. Title: Growth of groups of wind generated wavesSpeaker: Frederique DrullionInstitution: Embry-Riddle Aeronautical UniversityEmail: Frederique.Drullion@erau.edu

Abstract: A high-Reynolds-number stress closure model is used to perform numerical simulations of the windflow above different groups of waves. The group profiles can change as the individual waves grow within itsenvelop due to the energy transfer between the wind and the group. The focus of this study is the behavior ofthe critical layer and the associated “cat’s-eye” structures centered around the critical height, where the realpart of the complex wave speed is equal to the mean flow velocity. The position and size of these structuresdepend on the wave age and the wave steepness. It is shown that the larger the structures become, the moredisturbance of the wind flow above the wave occurs. The results obtained here demonstrate the formation ofcat’s-eye structures which appear asymmetrically over the waves within a group.

25. Title: A Risk Structured Mathematical Model of Buruli Ulcer Disease in GhanaSpeaker: Christina EdholmInstitution: University of Tennessee, KnoxvilleEmail: cedholm@utk.eduCo-author(s): Benjamin Levy, Ash Abebe, Theresia Marijani, Scott Le Fevre, Suzanne Lenhart, Abdul-AzizYakubu, Farai Nyabadza

Abstract: We constructed a model to study infectious diseases with environmental transmission from apathogen. The model considered two risk groups of susceptible individuals, based on level of interaction withthe environment. Our model and results were applied to the case of Buruli ulcer disease, a debilitating diseaseinduced by Mycobacterium ulcers. The bacteria is know to live in water environments, though the exact trans-mission mechanism is currently undetermined. We parameterized our model for cases in Ghana and performeda global sensitivity analysis. Our model and case study provide insight into the importance of ’low’ and ’high’risk groups on transmission dynamics.

26. Title: Application of nonstandard finite difference method to three compartment pharmacokinietics modelsSpeaker: Oluwaseun Francis EgbelowoInstitution: University of the WitwatersrandEmail: oluwaseun@aims.edu.ghCo-author(s): Charis Harley, Byron Jacobs

Abstract: The complex nature of the analytical solutions to three compartment pharmacokinetic lead todiscrete approximation of the continuous differential equation been mostly used. In this paper, we derivednonstandard finite difference scheme for three-compartment pharmacokinetic models. For the case when thesystem is homogeneous (models arising from IV bolus injection mode of administration), we give exact finitedifference scheme while in the case of non-homogeneous (models arising from IV infusion route of administration),we provide scheme that has the same qualitative behaviour as the analytical solution for all step-sizes. Resultsof numerical experiments are presented.

27. Title: A two pathways model for chemotactic signaling in Azospirillum brasilenseSpeaker: Mustafa ElmasInstitution: University of Tennessee, KnoxvilleEmail: elmas@math.utk.eduCo-author(s): Tanmoy Mukherjee, Vasilios Alexiades, Gladys Alexandre

Abstract: Bacteria use a mechanism that enables them efficiently and rapidly respond to a wide range ofbackground environment changes, moving towards favorable and away from toxic environment by altering thefrequency of flagella switching. This behavior is known as Chemotaxis The regulation of chemotaxis in bacteria isachieved by a network of interaction proteins, chemotaxis signal transduction pathway. It has been recently foundthat majority of motile bacteria have two or more (Che) systems whereas the model organism, Escherichia coli,possesses only a single chemotaxis system. In this talk, we present a novel mathematical model that can be usedto understand the properties of biological signaling pathways in Azospirillum brasilense and their connectivity.

28. Title: Mathematical modelling of within-host dynamics of cholera: bacterial viral interactionSpeaker: Abdulahi Opeyemi FALADEInstitution: African Institute for Mathematical Sciences, AIMS-SenegalEmail: abdulahi.o.falade@aims-senegal.orgCo-author(s): Farai Nyabadza, University of Stellenbosch, South Africa

Abstract: In this paper work, we modified non-linear deterministic model system proposed in X. Wang andJin. Wang work by defining a specific function for intrinsic growth of human vibrios and the virus for betterunderstanding of withinhost dynamics of cholera: bacterial-viral interaction. We determine the positivity of thesolutions and invariant region where the solutions are biologically meaningful and mathematically well-posed.The basic reproduction number R0 is computed and established as a sharp threshold for disease dynamics: whenR0 < 1, the highly infectious vibrios will not grow within the human host and the environmental vibrios ingestedwill not cause cholera infection: when R0 > 1, the human vibrios will grow and persist, leading to human cholera.With the derived basic reproduction number R0, the infection free and unique endemic equilibrium is found tobe globally asymptotically stable. Analytically, most sensitive parameter is intrinsic growth rate of the humanvibrios. Numerical simulation results are used to validate our analytical prediction. Additionally, we obtainedresult for periodic ingested rate of environmental vibrios at R0 < 1 only. Keywords: Cholera model; within-hostdynamics; basic reproduction number; disease threshold; global asymptotic stability; bacterial-viral interaction.

29. Title: Logarithmic, well-posed approximation of the backward heat equation in Lp spaces, 1 < p <∞Speaker: Matthew FuryInstitution: Penn State AbingtonEmail: maf44@psu.edu

Abstract: Consider the abstract Cauchy problem du/dt = Au, u(0) = x, 0 < t < T , where −A generatesa holomorphic semigroup of angle π/2 on a Banach space. We show that the well-posed problem defined byBoussetila and Rebbani’s approximation fβ(A) = − 1

qT ln(β + e−qTA), 0 < β < 1, q ≥ 1, provides a method forregularizing the original ill-posed problem in this setting. The logarithmic approximation has been consideredrecently, especially for non-linear problems in Hilbert space; also Huang applies the approximation in Banachspace. Our work provides new calculations in Banach space so as to include the Laplace operator defined on Lp

spaces, 1 < p <∞, thereby establishing regularization for the backward heat equation.

30. Title: Least Action Methods and Noise Induced Transitions in Periodically Forced SystemsSpeaker: John GemmerInstitution: Wake Forest UniversityEmail: gemmerj@wfu.eduCo-author(s): Yuxin Chen, Mary Silber, Alexandria Volkening, Jessica Zanetell

Abstract: We present a study of the metastability of periodic orbits for periodically forced systems perturbedby weak additive noise. We are particularly interested in how deterministic properties of the underlying ordinarydifferential equation determine the most probable ”tipping times” between basins of attraction. For autonomoussystems the Freidlin-Wentzell theory of large deviations provides a framework for understanding such rare eventsin the singular limit of vanishing noise strength. However, for non-autonomous systems such a universal resultis lacking. One difficulty is that in contrast with autonomous systems there are three relevant time scales: theperiod of the forcing, relaxation time to metastable states, and Kramer’s time of escape in the absence of forcing.Using least action techniques applied to the Onsager-Machlup functional we systematically study how these time

scales as well as the geometry of the vector fields control the most probable tipping time. While at this stagemany of our results at are numerical, we are able to prove precise results in the limit of infinite forcing periodusing the technique of gamma-convergence.

31. Title: Existence and Uniqueness of Measure Valued Solutions to a Hyperbolic Conservation Law with In-fluxand Out-fluxSpeaker: Xiaoqian GongInstitution: Arizona State UniversityEmail: xgong14@asu.eduCo-author(s): Matthias Kawski

Abstract: Motivated by practical control problems in highly re-entrant semiconductor manufacturing systems,we study the evolution of measures in the space B([0, 1]) of finite Borel measures. In particular, we investigatethe well-posedness of a Cauchy problem directed by a scalar hyperbolic conservation law, which is characterizedby the nonlocal dependence of the velocity on the state. Our setting is distinguished by bounded domain within-flux and out-flux and thus not necessarily constant mass and possible discontinuities of the velocity withrespect to time. We also develop a suitable concept of solutions to the chosen problem and prove the existenceand uniqueness of the measure solutions.

32. Title: Some existence results for systems of second-order impulsive differential equationsSpeaker: John R. GraefInstitution: University of Tennessee at ChattanoogaEmail: john-graef@utc.edu

Abstract: The existence of solutions to systems of nonlinear second order impulsive differential equationsis established by using vector versions of Perov’s fixed point theorem combined with a technique based onvector-valued metrics and matrices that converge to zero.

33. Title: Modeling Distinct Virus Infection Strategies in Virus-Microbe SystemsSpeaker: Hayriye GulbudakInstitution: University of Louisiana at LafayetteEmail: hayriye.gulbudak@louisiana.eduCo-author(s): Joshua S. Weitz, Georgia Institute of Technology

Abstract: Viruses of microbes, including bacterial viruses (phage), archaeal viruses, and eukaryotic viruses,can influence the fate of individual microbes and entire populations. Here, we model distinct modes of virus-hostinteractions and study their impact on the abundance and diversity of both viruses and their microbial hosts.We consider two distinct viral populations infecting the same microbial population via two different strategies:lytic and chronic. A lytic strategy corresponds to viruses that exclusively infect and lyse their hosts to releasenew virions. A chronic strategy corresponds to viruses that infect hosts and then continually release new virusesvia a budding process without cell lysis. The chronic virus can also be passed on to daughter cells during celldivision. The long-term association of virus and microbe in the chronic mode drives differences in selectivepressures with respect to the lytic mode. We utilize invasion analysis of the corresponding nonlinear differentialequation model to study the ecology and evolution of heterogenous viral strategies. We first investigate stabilityof equilibria, and characterize oscillatory and bistable dynamics in some parameter regions. Then, we derivefitness quantities for both virus types and investigate conditions for competitive exclusion and coexistence. Inso doing we find unexpected results, including a regime in which the chronic virus requires the lytic virus forsurvival and invasion.

34. Title: Numerical Solutions of Time-Dependent Partial Differential EquationSpeaker: Daniel GuoInstitution: University of North Carolina at WilmingtonEmail: guod@uncw.edu

Abstract: One-step semi-Lagrangian forward method is investigated for computing the numerical solutionsof time-dependent partial differential equations with initial and boundary conditions. This method is based onLagrangian trajectory or the integration from the departure points (regular nodes) to the arrival points. Thearrival points are traced forward from the departure points along the trajectory of the path. Most likely thearrival points are not on the regular grid nodes. The techniques of classic Runge-Kutta methods are employed

for the computations of arrival points and solutions. The convergence and stability are studied for the explicitmethods. The numerical examples show that those methods work very efficient for the time-dependent partialdifferential equations.

35. Title: Mathematical modeling of nonlinear convection induced by the sequestration of carbon dioxide in ageological formationSpeaker: Layachi HadjiInstitution: The University of AlabamaEmail: lhadji@ua.edu

Co-author(s): Liet A. Vo

Abstract: In this talk, we examine a new way at modeling the problem of convection that occurs during thegeological sequestration of carbon dioxide. The mathematical model accounts for both diffusion and convectionin a geological formation that has anistropic permeability and anisotropic carbon diffusion. The permeability ismodeled as a decaying exponential to describe its slow decrease with depth. We also account for a first orderreaction between CO2 and the porous medium. We investigate the onset of convection and its weakly nonlinearevolution. We consider a base state that mimics a Rayleigh-Taylor configuration with a carbon-rich heavy layeroverlying a carbon-free lighter layer and determine the thickness at which the configuration becomes unstable.The analysis is performed using the classical normal modes and the weakly nonlinear analysis is performed usinglong-wavelength asymptotics. We derive the threshold instability conditions and associated flow patterns. Ouranalysis leads to the derivation of the convective flux conditions at the interface and the resulting fingeringpatterns. Finally, we put forth the conditions expressed in terms of formation and fluid parameters for the onsetof convective shutdown.

36. Title: Mathematical Modeling of the Breakup of a Slender Fluid Jet with Variable Surface TensionSpeaker: Muhammad HameedInstitution: University of South Carolina UpstateEmail: mhameed@uscupstate.edu

Abstract: The influence of surfactant on the breakup of a periodic fluid jet of low viscosity immersed inhighly viscous exterior fluid at low Reynolds number is studied. With an aim to better understand the pinch-offdynamics, we use slender body theory, numerical simulations and experimental studies to investigate the effect ofsurfactant on the necking and breakup. Evolution equations for the jet interface and surfactant concentration arederived using long wavelength approximations. These one dimensional partial differential equations are solvednumerically for given initial interface and surfactant concentration. It is found that the presence of surfactant atthe interface retards the pinch-off process. The influence of various physical effects on the breakup process is alsoinvestigated. Surface diffusion of surfactant and surfactant solubility are found to have significant influence onthe instability of the thread. The influence of surface diffusion of surfactant on the thread deformation is studiedby varying surface Peclet number. It is found that greater diffusion of surfactant causes the jet to pinch faster.Surfactant solubility is found to have similar effect. Results of the long wavelength model are also comparedagainst the numerical simulations of the full problem. The solution of the full problem shows similar behaviorto the simplified model. It is found that the equation of state does not have much effect on the breakup. Theexperimental results support the prediction of theoretical model that the presence of surfactant slows down thepinch-off process.

37. Title: Localization of eigenfunctions on quantum graphsSpeaker: Evans M. Harrell IIInstitution: Georgia TechEmail: harrell@math.gatech.eduCo-author(s): Anna V. Maltsev, Queen Mary University, London

Abstract: I’ll discuss ways to construct realistic “landscape functions” for eigenfunctions ψ of quantum graphs.This term refers to functions that are easier to calculate than exact eigenfunctions, but which dominate |ψ| ina non-uniform pointwise fashion constraining how ψ can be localized. Our techniques include Sturm-Liouvilleanalysis, a maximum principle, and Agmon’s method.

38. Title: On improving isoperimetric inequalities for the fundamental tone of a vibrating membraneSpeaker: Lotfi HermiInstitution: Florida International UniversityEmail: lhermi@fiu.edu

Abstract: In the talk we will specifically motivate, conjecture, and prove an isoperimetric inequality relatingthe fundamental eigenvalue of a wedge-like membrane to its relative torsional rigidity. This new sharp inequalityimproves the Faber-Krahn and Payne-Weinberger inequalities for such domains. This will demonstrated numer-ically for special domains, as well. The central tool of this recent development is the use of a new weighted formof the Kohler-Jobin symmetrization method, which we introduce.

39. Title: Blowup rate for rotational nonlinear Schroedinger equationsSpeaker: Yi HuInstitution: Georgia Southern UniversityEmail: yihu@georgiasouthern.eduCo-author(s): Nyla Basharat, Augusta University; Shijun Zheng, Georgia Southern University

Abstract: We will present a blowup rate of solutions to nonlinear Scroedinger equations with harmonic po-tential and a rotation term. We will prove that there is the ”log-log law” if the initial data satisfies some massand energy hypotheses. We also discuss some other related results.

40. Title: Solutions to a First Order Hyperbolic SystemSpeaker: Nezam IraniparastInstitution: Western Kentucky UniversityEmail: nezam.iraniparast@wku.edu

Abstract: The study of small perturbations in the shock initiation of an inviscid compressible fluid withchemical reaction leads to a first order hyperbolic system of two equations. The order zero approximation of thesystem involves only constant coefficients. Here, we study a variation of this hyperbolic system and generalize itso that not all coefficients are constants. The boundary conditions in the first quadrant (t, x > 0), where x is thespatial variable and t is time, include data along x = 0 and a proportionality relation between the dependentvariables along t = 0. Using the characteristics of the system, we obtain explicit solutions.

41. Title: Bounded solutions of a Volterra integrodifferential equationSpeaker: Muhammad IslamInstitution: University of DaytonEmail: mislam1@udayton.eduCo-author(s): Nasrin Sultana

Abstract: In this article the existence of a continuous and bounded solution of a nonlinear Volterra integrod-ifferential equation is studied. In the analysis, Schaefer’s fixed point theorem and Liapunov’s direct method areemployed. The existence of a continuous and bounded solution is shown using Schaefer’s fixed point theorem,which requires an a priori bound on all such solutions of an auxiliary equation. Liapunov’s direct method is thenapplied to obtain such an a priori bound.

42. Title: Modeling Agal BloomsSpeaker: Hem JoshiInstitution: Xavier UniversityEmail: joshi@xavier.eduCo-author(s): Mark Miller

Abstract: We propose a simple relationship between algal species and Zebra Mussel through a basic ecologicalpredator-prey model: the Lotka-Volterra model. Through this model, we can learn what level of Zebra Musselpopulation will minimize the presence of algal populations. Then, the economic impact of the bloom will beassessed, as well as a potential solution to achieve the necessary decrease in phosphorus loading needed tosufficiently reduce the risk of compromising the water supply of the populations that depend on the WesternBasin of Lake Erie.

43. Title: Two type Lyapunov-Krasovskii Characterizations of Input-to-Output Stability for Systems with DelaysSpeaker: Hasala Senpathy Gallolu KankanamalageInstitution: Roger Williams UniversityEmail: hgallolu@rwu.eduCo-author(s): Yuan Wang, Yuandan Lin

Abstract: In this work we present Lyapunov-Krasovskii characterizations of two different types for outputstability of systems with delay affected by disturbances given as follows:

x′(t) = f(xt, u(t)),

x(s) = ξ(s), −θ ≤ s ≤ 0

y(t) = h(x(t)),

where xt : [−θ, 0]→ Rn is given by xt(s) = x(t+ s), θ > 0 is a constant and the measurable, locally essentiallybounded function u represents an input (control) to the system. We obtain two Lyapunov characterizations ofoutput stability, by using two types of Lyapunov-Krasovskii functionals with different decay estimates. One of thetypes is motivated by delay-free context and the second type is tailor-made for systems with delays. Furthermore,two types simultaneously provide versatality in wide range of applications and in theoretical framework as well.Special cases of current results include Lyapunov-Krasovskii characterizations of Global Asymptotic stabilityand Input-to-State stability that provides better view for existing results in the literature.

44. Title: On a discrete fourth order boundary value problemSpeaker: Lingju KongInstitution: University of Tennessee at ChattanoogaEmail: Lingju-Kong@utc.edu

Abstract: Several criteria for the existence of one and multiple solutions are established for a discrete fourthorder boundary value problem. The proofs of the theorems are mainly based on the variational method andcritical point theory. Examples are presented to illustrate the results.

45. Title: A Summer Undergraduate Research Project in Fractional Difference EquationsSpeaker: Curtis KunkelInstitution: University of Tennessee MartinEmail: ckunkel@utm.edu

Abstract: A 10-week undergraduate research project was completed this last summer with two undergraduatestudents. Topics discussed began with Fractional Calculus and continued through Fractional Difference Equa-tions. A discussion will be on the process used and the references investigated, along with ideas on best practicesfor keeping the project moving.

46. Title: On Periodicity of Solutions of an Impulsive Differential Equation with Piecewise Constant ArgumentsSpeaker: Mehtap LafcıInstitution: Ankara University, TurkeyEmail: mlafci@ankara.edu.tr

Abstract: In this talk, we consider a first order nonlinear impulsive differential equation with piecewise constantarguments and we use Carvalhos method to obtain some conditions for the existence of nonconstant periodicsolutions of this equation. Also, we give examples to illustrate our results.

47. Title: Drift-diffusion threshold models for the analysis of cellular decisionsSpeaker: Rachel LeanderInstitution: Middle Tennessee State UniversityEmail: rachel.leander@mtsu.eduCo-author(s): Zack Jones, Darren Tyson, Leonard Harris, Vito Quaranta

Abstract: Many cellular decisions, including the decisions to divide and die, are subject to considerable vari-ability. This variability has the potential to provide significant insights into cellular decision-making processes,provided suitable statistical/mathematical models exist. In this talk, I will discuss the use of drift-diffusion-threshold models for the analysis of decision-time data on cell death and division and illustrate the informationthat these models can provide with specific examples.

48. Title: Nonlinear Modulational Instability of Dispersive PDE ModelsSpeaker: Shasha LiaoInstitution: Georgia Institute of TechnologyEmail: sliao7@gatech.eduCo-author(s): Jiayin Jin, Zhiwu Lin

Abstract: The modulational instability, also called Benjamin-Feir or side-band instability the literature, is avery important instability mechanism in lots of dispersive and fluid models. Various conditions for linear modu-lational instability have been derived for different dispersive wave models including Fractional KDV equations,Whitham etc. In this talk, we present some recent progress on the nonlinear modulational instability of KDVtype equations. The instability is considered under both periodic and localized perturbations.

49. Title: An Efficient Numerical Method for Electromagnetic Scattering in Random MediaSpeaker: Cody LortonInstitution: The University of West FloridaEmail: clorton@uwf.edu

Abstract: In this talk I will discuss an efficient Monte Carlo interior penalty discontinuous Galerkin (MCIP-DG) method for the time-harmonic Maxwell’s equations in “weakly” random media. Such media takes the formof a random perturbation of some homogeneous media. Wave number explicit solution estimates are established.It is also shown that the solution possesses a multi-modes representation which takes the form of a power seriesin the perturbation parameter. Each mode function used in the multi-modes representation is shown to satisfya “nearly deterministic” recurrence system of partial differential equations. This recurrence system is said tobe “nearly deterministic” in the sense that any randomness appears in the right-hand side source terms andnot in the coefficients of the PDEs. In addition, each “nearly deterministic” PDE involves the same differentialoperators. An unconditionally stable IP-DG method for the deterministic time-harmonic Maxwell’s equationsalong with a Monte Carlo method are combined with this multi-modes representation to obtain an MCIP-DGmethod for resolving the solution. An efficient algorithm for resolving the solution is obtained by combining thismulti-modes MCIP-DG method with an LU-direct solver. The error associated to this algorithm is analyzed andestimates are provided which depend on the mesh size h, the sampling number M , and the number of modesN .

50. Title: Differential Equations of Dynamical OrderSpeaker: Andrei LuduInstitution: Embry-Riddle Aeronautical UniversityEmail: ludua@erau.eduCo-author(s): Harihar Khanal

Abstract: We introduce a special type of ODE with variable order of differentiation depending continuously onthe independent variables, time or space. We solve such dynamical order of differentiation equation (DODE) asVolterra integral equations of second kind with singular integrable kernel. We present the theorems for existenceand uniqueness of these deformed solutions. We show examples of numerical approach and solutions for DODEtransitioning from order 1 to 2 and back, and the comparison with the classic ODE corresponding solutions. Weintroduce dynamical order differential forms with their exact chains of cohomology, and we introduce by dualitya new axiomatic approach on manifold boundaries of variable, non-integer dimension with possible applicationin the theory of adjacent possible.

51. Title: Nonlinear Sturm-Liouville problems with nonlocal boundary conditionsSpeaker: Dan MaroncelliInstitution: College of CharlestonEmail: maroncellidm@cofc.eduCo-author(s): Jesus Rodriguez

Abstract: In this talk, we will discuss the existence of solutions to nonlinear Sturm-Liouville problems withnon-local boundary conditions.

52. Title: Mathematical modelling vector-borne diseasesSpeaker: Dephney MathebulaInstitution: University of VendaEmail: dephneymathebula@yahoo.com

Abstract: In this study, we develop the mathematical model that monitors the transmission dynamics ofschistosome parasite in two different environments, namely, physical water environment and physical land en-vironment. We take into account the water environment because that is where the intermediate host (snail) ofthe schistosome parasite breeds. The model will assist in identifying the parameters to be targeted for controlmeasures implementation. We also incorporate sanitation into the basic model. We investigated the mathemat-ical properties of the model. We established that the model is mathematically and epidemiologically well-posed.Numerical analysis results suggest that the environmental parameters and human behaviour have an effect inthe spread of the schistosome parasite, as such, the control measures have to focus more on the environmentalparameters, like providing human population with proper sanitation. The results for the model with sanitationsuggest that promoting good environmental sanitation practices and improved infrastructure for human wastedisposal associated with construction and use of toilets alone can not eradicate the spread of schistosomiasis.They need to be coupled with health education campaign and treatment and other environmental disease controlmechanisms.

53. Title: Modeling different protocols of dendritic cell therapy for melanomaSpeaker: Hugh MatlockInstitution: Middle Tennessee State UniversityEmail: hbm2z@mtmail.mtsu.eduCo-author(s): J. Angela Murdock, Khem Poudel, Zachariah Sinkala, Jacy Zanussi

Abstract: Dendritic cells are a promising immunotherapy tool for boosting an individual’s antigenspecificimmune response to cancer. Different protocols exist for administering this therapy and our model analyzesthe efficacy of these protocols. We use differential and delay-differential equations to describe the interactionsbetween dendritic cells, effector-immune cells, and tumor cells. We account for the trafficking of immune cellsbetween spleen, blood, and tumor compartments. Our model validates some experimental results for dendritictherapy in mice in the literature.

54. Title: Approximate Solution to the ODE Modeling Thermal Expulsion of Fluid From a Slender Heated TubeSpeaker: Ronald E. MickensInstitution: Clark Atlanta UniversityEmail: rmickens@cau.edu

Abstract: The following boundary-value problem arises in the investigation of the thermal expulsion of hotfluid from a slender heated tube [1]

y′′(z) = y(z)[y(z)− zy′(z)], y′(0) = −√

3, y(∞) = 0 (1)

With this information, the goal is to determine the value y0 = y(0). To date, no purely analytic procedure hasaccomplished this task. Using a variety of exact results known for y(z), we show that the following functionalform

y(z) =A

1 +Bz + Cz2(2)

provides an “accurate” approximation to the solution of Eq. (1), with y(0) having the value 1.5376.References: [1] Lawrence Dresner, Similarity Solutions of Partial Differential Equations (Pitman, Boston,1983). See Section 4.7.

55. Title: Optimal control of vaccination in a PDE model for Zika virusSpeaker: Tiago MiyaokaInstitution: University of Tennessee KnoxvilleEmail: tiagoyuzo@gmail.com

Abstract: We developed a reaction diffusion PDE compartmental model to study the spread of Zika virus, usingSIR (susceptible – infectious – removed) dynamics for humans and SI (susceptible – infectious) for mosquitoes.Vaccination is applied to the human population using optimal control theory, moving humans from susceptibleto removed (immune) class. We use data from 2015 infected human cases in the state of Rio Grande do Norte

in Brazil to parametrize the model, and then explore numerical simulations. This work is a collaboration withSuzanne Lenhart and Joao Meyer.

56. Title: Seasonal Effects on Sources and Large Mouth Bass Predation in Normandy LakeSpeaker: J. Angela Hart MurdockInstitution: Middle Tennessee State UniversityEmail: Julie.Murdock@mtsu.eduCo-author(s): Hugh Matlock, Khem Poudel, Zachariah Sinkala, Jacy Zanussi

Abstract: Survival and predation of algae colonies and juvenile small fish is an important question for TennesseeDepartment of the Environment and Conservation (TDEC), Tennessee Wildlife Resource Agency, (TWRA),Tennessee Valley Authority (TVA) and conservation officials as they are tasked to maintain healthy waterwaysfor a range of uses. The agencies collected large amounts of population data yet there has been little quantificationof the changes in vulnerability of juvenile small fish to specific predators i.e black bass that may result fromseasonal management decisions (artificial habitats creation, additional fingerlings from fisheries). We analyzea simple predator-prey model for three species. Next we assume the species have logistic growth. finally weinclude an Allee effect on the predators. The models have several applications. For instance, the model canprovide information to improve wildlife management decisions.

57. Title: Monotone Method for Finite System of Riemann-Liouville Sequential Fractional Differential Equationswith Periodic Boundary ConditionsSpeaker: Jagdish A. NanwareInstitution: Shrikrishna Mahavidyalaya, Gunjoti-413605, Dist.Osmanabad (M.S)-INDIAEmail: jag skmg91@rediffmail.com

Abstract: Monotone method coupled with lower and upper solutions is developed for finite system of Riemann-Liouville sequential fractional differential equations with periodic boundary conditions. It is successfully appliedto obtain existence and uniqueness of solutions finite system of Riemann-Liouville sequential fractional differentialequations.

58. Title: Stationary solutions of reaction-diffusion equations with unilateral regulationsSpeaker: Josef NavratilInstitution: Czech Technical University in PragueEmail: pepa.navratil@gmail.com

Abstract: The pattern formation in reaction-diffusion systems is a popular and intensively studied phenomenonin mathematical biology. If Turing conditions are fulfilled in a system of two chemicals, the diffusion driveninstability leads to a formation of pattern. However, these conditions require the diffusion rates of chemicals tobe significantly different. The main motivation of the presented research was to describe bifurcation from zeroof stationary solutions (patterns) in reaction-diffusion systems

d14u+ f(u, v) = 0

d24v + g(u, v) + h−(x, v−)− h+(x, v+) = 0

∂u

∂~n=∂v

∂~n= 0 on ∂Ω,

defined in a bounded set Ω with a Lipschitz boundary ∂Ω, where u, v represent a deviation of concentrationfrom the homogeneous steady state, f, g are real functions representing kinetic terms satisfying the conditions ondiffusion-driven instability, and h+, h− represent a unilateral regulations (sources). The presence of unilateralregulation leads to the existence of non-homogeneous solutions (patterns) even for diffusion rates, for whichthere are only homogeneous solutions in systems without unilateral sources. The existence of solutions for suchparameters was proved by finding bifurcation points and branches of solutions bifurcating from zero using themethods of nonlinear analysis, namely Implicit Function Theorem and Variational Methods, see [2], [3]. Thebiological motivation and a physical meaning of studied systems will also be shortly discussed. The numericalexperiments, see [1], show that these new patters are irregular.References[1] T. Vejchodsky, F. Jaros, M. Kucera, V. Rybar: Unilateral regulation breaks regularity of Turing patterns,Physical Review E 96, 2017, 022212-.[2] L. Recke, M. Vath, M. Kucera, J. Navratil, Crandall-Rabinowitz Type Bifurcation for Non-DifferentiablePerturbations of Smooth Mappings, in Patterns of Dynamics, Berlin, 25.7. 2016 – 29.7.2016, editors: Gurevich,

P. – Hell, J. – Sandstede, B. – Scheel, A., Springer Proceedings in Mathematics & Statistics, Springer, Cham,2017.

[3] M. Kucera, J. Navratil: Eigenvalues and bifurcation for problems with positively homogeneous operatorsand reaction-diffusion systems with unilateral terms, submitted, preprint available online:http://www.math.cas.cz/fichier/preprints/IM 20170901142214 93.pdf

59. Title: Solutions of Boundary Value Problems at Resonance with Periodic and Antiperiodic Boundary ConditionsSpeaker: Jeffrey T. NeugebauerInstitution: Eastern Kentucky UniversityEmail: jeffrey.neugebauer@eku.eduCo-author(s): Aldo Garcia

Abstract: We study the existence of solutions of the second order boundary value problems at resonancey′′ = f(t, y, y′) satisfying the boundary conditions y(0) + y(1) = 0, y′(0) − y′(1) = 0 or y(0) − y(1) = 0,y′(0) + y′(1) = 0. These problems are both at resonance, so we employ a shift method. Fixed point methods arethen used to show the existence of solutions.

60. Title: Spectral asymptotics of some one-dimensional fractal LaplaciansSpeaker: Sze-Man NgaiInstitution: Georgia Southern UniversityEmail: smngai@georgiasouthern.eduCo-author(s): Wei Tang, Yuanyuan Xie

Abstract: The spectral dimension of the Laplacian defined by a measure has been shown to be closely related toheat kernel estimates, which under suitable conditions determine whether wave propagates with finite or infinitespeed. We observe that some self-similar measures defined by finite or infinite iterated function systems withoverlaps satisfy certain “essentially finite type condition”, which allows us to extract useful measure-theoreticproperties of iterates of the measure. We develop a technique to obtain, under this condition, a closed formulafor the spectral dimension of the Laplacian. Earlier results for fractal measures with overlaps rely on Strichartzsecond-order identities, which are not satisfied by the measures we consider here. This is a joint work with WeiTang and Yuanyuan Xie.

61. Title: Local Sensitivity Analysis for 1D Poro-Elastic and Poro-Visco-Elastic ModelsSpeaker: Marcella NoormanInstitution: Center for Research in Scientific Computation, NC State UniversityEmail: mjnoorma@ncsu.eduCo-author(s): H.T. Banks, K. Bekele-Maxwell, L. Bociu, G. Guidoboni

Abstract: Poro-elastic and poro-visco-elastic models find many uses in biological applications for which bound-ary data plays a crucial role. A recent theoretical and numerical analysis of such systems has identified the timeregularity of the imposed boundary traction as a crucial factor in guaranteeing boundedness of solutions. Here,we extend this analysis by studying local sensitivities of the model solutions with respect to the boundary sourceof traction. We also consider local sensitivities with respect to the conditions imposed on Darcy velocity. Finally,to further investigate the role of viscosity, we compare results from the purely elastic case vs. the visco-elasticcase.

62. Title: Management Strategies in a Malaria Model Combining Human and Transmission-blocking VaccinesSpeaker: Eric NumforInstitution: Augusta UniversityEmail: enumfor@augusta.eduCo-author(s): Jemal Mohammed-Awel, Ruijun Zhao, Suzanne Lenhart

Abstract: A mathematical model studying control strategies of malaria transmission is formulated and an-alyzed. The existence of a backward bifurcation is established analytically in the absence of vaccination, andnumerically in the presence of vaccination. Optimal control strategies, using vaccination and vector control areinvestigated to gain qualitative understanding on how the combination of vaccination and vector control shouldbe used to reduce disease prevalence in a malaria endemic setting.

63. Title: Experimental and Numerical Investigation of a Flow-Leak SimulatorSpeaker: Cyril Okhio and Lance CrimmInstitution: Kennesaw State UniversityEmail: cokhio@kennesaw.eduCo-author(s): Kailani Redding, Blake Parr, Jennifer Folden, Tamara Franklin, Adeyinka Adebayo, Thuan Le

Abstract: The project described in this paper (Fluid Flow Leak Simulator) demonstrates how undergrad-uate students have utilized mathematical tools to model design, in everyday situations, and have carried outexperiments to validate their design.

64. Title: A model of a virtual community with a decentralized reputation-based peer evaluationSpeaker: Andrei OliferInstitution: Georgia Gwinnett CollegeEmail: aolifer@ggc.edu

Abstract: This study was motivated by the problem of identifying fake news on the Internet. To explorepossible solutions to this problem we introduce a model of a virtual community in which members submitdocuments and evaluate documents of others. Evaluators are selected according to their reputation. The modelis a system of ODEs for proportions of members with certain reputations. Analytical and computational resultssuggest the proposed evaluation mechanism is effective in a wide range of parameters and even in cases whensome members form cliques.

65. Title: Optimal control applied to a spatio-temporal anthrax modelSpeaker: Buddhi PanthaInstitution: Abraham Baldwin Agricultural CollegeEmail: bpantha@abac.eduCo-author(s): Judy Day, Suzanne Lenhart

Abstract: Anthrax is a fatal disease caused by a gram positive, spore forming bacteria called Bacillus anthracis.The disease is endemic to several national parks and one of the main causes of herbivore decline. Most anthraxinfected animals face inevitable death and each infected carcass deposits massive number of spores into thesurrounding environment. Thus, controlling new infections through vaccination and eliminating spread throughproper carcass disposal are the only feasible ways to effectively control the disease when an outbreak occurs. Inthis talk, a system made up of parabolic partial differential equations together with ordinary differential equationswill be presented and effect of the two most commonly used controls of vaccination and carcass disposal on diseasetransmission will be investigated. Some numerical results will also be presented.

66. Title: Analysis of Stagnation Point Flow of an Upper-Convected Maxwell FluidSpeaker: Joseph PaulletInstitution: Penn State BehrendEmail: jep7@psu.edu

Abstract: Several recent papers have investigated the two-dimensional stagnation point flow of an upper-convected Maxwell fluid by employing a similarity change of variables that reduces the governing PDEs to anonlinear third order ODE boundary value problem. In these previous works, the BVP was studied numericallyand several conjectures regarding the existence and behavior of the solutions were made. In this talk we attemptto mathematically verify these conjectures. We prove the existence of a solution to the BVP for all relevantvalues of the elasticity parameter. We also prove that this solution has monotonically increasing first derivative,thus verifying the conjecture that no “overshoot” of the boundary condition occurs. Uniqueness results areproved for a large range of parameter space and bounds on the skin friction coefficient are calculated.

67. Title: Super Time-Stepping Schemes for Conduction-Radiation Heat Transfer ProblemSpeaker: Benedict PineyroInstitution: Embry-Riddle Aeronautical UniversityEmail: pineyrob@my.erau.eduCo-author(s): Harihar Khanal

Abstract: We solve a nonlinear parabolic partial differential equation describing conduction-radiation heattransfer in a semitransparent medium (glass) numerically using an explicit finite volume method. To overcomethe stability restriction of the explicit method we employ two first order super time-stepping (STS) schemesbased on Chebyshev and Legendre polynomials and compare their performances.

68. Title: Modeling T cell proliferation in response to lung cancer in miceSpeaker: Khem PoudelInstitution: Middle Tennessee State UniversityEmail: knp4k@mtmail.mtsu.eduCo-author(s): Hugh Matlock, J. Angela Murdock, Zachariah Sinkala, Jacy Zanussi

Abstract: Cell proliferation is one common characteristic of biological systems. The immune system maintainsa body’s health by producing a continuous supply of diversified T lymphocytes in the thymus which involves sub-processes of proliferation, differentiation, selection, death and migration. To quantify cell proliferation dynamicsresearchers use specific experimental methods and mathematical modeling. Here, we consider the impact ofgenetics and aging on the immune system by investigating the dynamics of proliferation of T lymphocytes. Weuse ordinary differential equations to model the evolution of single T cell behavior. We fit model to the datafrom literature to deduce proliferation rates and estimate cell cycle durations in sub-populations. Our resultsquantify and support experimental data that T cell proliferation is heterogeneous and genetically dependent(specific to cell differentiation stages in thymus and spleen and is altered with age). Finally, our model quantifiesproliferation rates and cell cycle phase durations from complex experimental data, revealing T cell proliferationheterogeneity and specific signatures.

69. Title: Discretization Scheme In Volterra Integro-differential Equations That Preserves Stability and Bounded-nessSpeaker: Youssef RaffoulInstitution: University of DaytonEmail: yraffoul1@udayton.edu

Abstract: A nonstandard discretization scheme is applied to continuous Volterra integro-differential equa-tions. We will show that under our discretization scheme the stability of the zero solution of the continuousdynamical system is preserved. Also, under the same discretization, using a combination of Lyapunov func-tionals, Laplace transforms and z−transforms, we show that the boundedness of solutions of the continuousdynamical system is preserved.

70. Title: Monotone Method for Caputo Fractional Differential Equations with ImpulsesSpeaker: Diego RamirezInstitution: Savannah State UniversityEmail: ramirezd@savannahstate.edu

Abstract: In this presentation we define lower and upper solutions for impulsive differential equations withCaputo derivative of order q, 0 < q < 1, and initial condition. Next we use a comparison result and develop amonotone iterative technique to prove the existence of minimal and maximal solutions.

71. Title: Dirichlet Control Using Boundary Penalty Method for Unsteady Navier-Stokes EquationsSpeaker: S. S. RavindranInstitution: University of Alabama in HuntsvilleEmail: ravinds@uah.edu

Abstract: This paper is concerned with the analysis of the finite element approximations of Dirichlet controlproblem using boundary penalty method for unsteady NavierStokes equations. Boundary penalty method hasbeen used as a computationally convenient approach alternative to Dirichlet boundary control problems governedby Navier-Stokes equations due to its variational properties. Analysis of the mixed Galerkin finite element methodapplied to the spatial semi-discretization of the optimality system, from which optimal control can be computed,is presented. An optimal L-infinity(L2) error estimate of the numerical approximations of the optimality systemis derived. Feasibility and applicability of the approach are illustrated by numerically solving a canonical flowcontrol problem.

72. Title: Global weak solution of magnetohydrodynamic equations with partial dissipation and diffusionSpeaker: Dipendra RegmiInstitution: University of North GeorgiaEmail: dipendra.regmi@ung.edu

Abstract: Whether the classical solutions of two-dimensional incompressible ideal magnetohydrodynamic equa-tions can develop a finite time singularity (or globally regular for all time) from smooth initial data with finiteenergy is an outstanding open problem in fluid dynamics. We study magnetohydrodynamic equations to explorehow far one can go beyond this and still prove the global regularity. In this presentation, we discuss some of ourrecent results of MHD equations with partial dissipation and diffusion.

73. Title: Existence and Uniqueness of Solutions to infinite Dimensional Kuramoto ModelSpeaker: Sathyanarayanan RengaswamiInstitution: Middle Tennessee State UniversityEmail: sr3q@mtmail.mtsu.eduCo-author(s): Rachel N. Leander

Abstract: The Kuramoto model is system of ordinary differential equations that describes the emergence ofsynchrony in a finite population of nonlinear phase oscillators. An infinite dimensional version of the model, inwhich the population is described by a continuous density function, is also of interest. In this case, the modelis rephrased as a single nonlinear integro-partial differential equation (IPDE) which describes the evolution ofthe density of oscillators of a given natural velocity, at each point of the unit circle. We consider the existenceand uniqueness of solutions to this IPDE. As a first step towards the full proof, we consider the case in whichthe oscillators have zero natural velocity. We use an iterative process to define a sequence of solutions to relatedlinear IPDEs, deduce convergence, and show that the limit solves the original IPDE.

74. Title: A delay differential equation model of activation of endothelial nitric oxide synthaseSpeaker: Lake RitterInstitution: Kennesaw State UniversityEmail: lritter@kennesaw.eduCo-author(s): Carol Chrestensen, John Salerno

Abstract: Nitric oxide (NO) is a radical used in inter- and intra-cellular signaling, and regulation of NOserves several functions in the vasculature related to homeostasis, adaptation, and development. Endothelialnitric oxide synthase (eNOS) is the primary enzyme in the vasculature that synthesizes and regulates NO.Various enzymes, kinases and phosphatases, influence eNOS through phosphorylation and dephosphorylationof its amino acid sites. Evidence of oscillation between inactive and active states of eNOS has been detectedexperimentally consistent with feedback mechanisms in signal transduction. Here we consider a feedback modelof eNOS activation in the form of a system of coupled ordinary differential equations. By the introduction oftime delays, we account for the more complex dynamics of a signal cascade (formation of protein complexes,diffusion, interactions of unspecified intermediaries, etc.). Under conditions on the model parameters, varyingthe time delay may give rise to a Hopf bifurcation. Properties of resulting oscillatory solutions are discussed.

75. Title: Eigencurves for the two-parameter Robin-Steklov eigenproblem for the LaplacianSpeaker: Mauricio A. RivasInstitution: University of North Carolina GreensboroEmail: marivas@uncg.edu

Abstract: This talk will outline the analysis of eigencurves associated with the two-parameter Robin-Stekloveigenproblem for the Laplacian. This is a special case of, and exemplifies, the general problem of studyingeigencurves associated with a triple (a, b, m) of continuous symmetric bilinear forms on a real Hilbert spaceV. For the special case of this presentation, variational characterizations of associated eigencurves, as well asorthogonality results for corresponding eigenspaces, are described. Regularity and asymptotic properties forthese eigencurves are discussed. These results lead to a geometrical description of the eigencurves. This is jointwork with Stephen B. Robinson.

76. Title: Characterizing the Fucik Spectrum for the p-LaplacianSpeaker: Stephen B RobinsonInstitution: Wake Forest UniversityEmail: sbr@wfu.edu

Abstract: We consider the boundary value problem

−∆pu = α|u|p−2u+ − β|u|p−2u− in Ω,u = 0 on ∂Ω,

where ∆pu := −∇ · (|∇u|p−2∇u) for p > 1, Ω is a smooth bounded domain in RN , u± := max±u, 0, and(α, β) ∈ R2. When this problem has a nontrivial solution, then (α, β) is an element of the Fucik Spectrum,Σ. Our main result is to provide the variational characterizations of several curves in Σ. Our results extendprevious work of the authors for the case p = 2, and extend the work of Perera for the general case.

77. Title: Noise induced mixed-mode oscillations in a stochastic predator-prey system with two time-scalesSpeaker: Susmita SadhuInstitution: Georgia College and State UniversityEmail: susmita.sadhu@gcsu.eduCo-author(s): Christian Kuehn

Abstract: We study the effect of demographic stochasticity, in the form of Gaussian white noise in a predator-prey model with two distinct time-scales. We model the birth-death process of the species as a continuous-timeMarkov process and derive a system of stochastic slow-fast Ito stochastic differential equations. For a suitableparameter regime, the deterministic drift part of the model admits a folded node singularity and exhibits asingular Hopf bifurcation. We transform the model into its normal form near the folded-node singularity whichcan be then used to understand the interplay between deterministic and stochastic small amplitude oscillations.The stochastic model admits several kinds of noise driven mixed-mode oscillations that capture the intermediatedynamics between two cycles of population outbreaks of the prey. We perform numerical simulations to studythe distribution of the random number of small oscillations between two large oscillations, which can be relatedto the return time between the outbreaks. Depending on the noise intensity and the distance to the Hopfbifurcation, we find that the distributions of the small oscillations resemble the 1200 years record on the returntimes of larch budmoth outbreak events in the subalpine larch forests in the European Alps.

78. Title: Dynamics of Fractional Differential Systems with Riemann-Liouville and Hadamard DerivativesSpeaker: Shahzad SarwarInstitution: Shanghai University, Shanghai, ChinaEmail: shahzadppn@gmail.comCo-author(s): Changpin Li

Abstract: In this talk, we consider the fractional dynamical system with Riemann-Liouville and Hadamardderivatives. Firstly, we present some results on these fractional dynamical systems defined by fractional differen-tial equations (FDEs) with Riemann-Liouville and Hadamard derivatives. Secondly, we define the correspondingfractional flows under suitable conditions. Then we prove linearization theorems for nonlinear fractional dynam-ical systems which have never been studied before.

79. Title: Wellposedness of a Nonlocal Nonlinear Diffusion Equation of Image ProcessingSpeaker: Yuanzhen ShaoInstitution: Georgia Southern UniversityEmail: yshao@georgiasouthern.eduCo-author(s): Patrick Guidotti

Abstract: In this talk, we will establish the wellposedness of a degenerate regularization of the well-knownPerona-Malik equation in noise reduction for discontinuous initial data. We will also show the (exponential)asymptotic stability of stationary solutions.

80. Title: On the numerical solutions of 2D Boussinesq equations with fractional dissipationSpeaker: Ramjee SharmaInstitution: University of North GeorgiaEmail: ramjee.sharma@ung.edu

Abstract: In this talk we will present the numerical computations of 2D Boussinesq equations with fractionaldissipation. A parallel pseudospectral method is developed and implemented for the computation. Given smoothinitial data, whether the solutions of the system with all the possible values of the parameters develop finite timesingularity or not is yet to be known. This issue is addressed by presenting the evolution of geometry of the levelcurves, energy spectra and associated norms of two major quantities involved in the system. The solutions werecomputed for different values of parameters. Some of the numerical solutions presented here strongly indicatepotential singularity in finite time suggesting a need for further investigations.

81. Title: A Graph-Theoretic Approach to the Construction of Lyapunov FunctionSpeaker: Zhisheng ShuaiInstitution: University of Central FloridaEmail: shuai@ucf.edu

Abstract: The graph-theoretic approach has become a standard method to construct global Lyapunov func-tions for large-scale differential equation systems. Appropriate graph/network design and reduction is the key inthe successful application of the approach. We illustrate these graph/network techniques using various modelsin the literature.

82. Title: A dynamical system model of a locally advanced non-small cell lung cancer with chemo-radiotherapySpeaker: Zachariah SinkalaInstitution: Middle Tennessee State UniversityEmail: Zachariah.Sinkala@mtsu.eduCo-author(s): Hugh Matlock, J. Angela Murdock, Khem Poudel, Jacy Zanussi

Abstract: In this paper, we develop a dynamical system model of locally advanced non-small cell lung cancertumor( NSCLC) response to the immune system. We extend this model to study the effects chemoradiationfor NSCLC on the system by studying how the temporal changes in human spleen volume affects changes inimmune parameters. The importance of the results has potential application in predicting patient’s outcome orthe efficacy of chemo-radiotherapy.

83. Title: Blow-up Continuity in Mean Curvature FlowSpeaker: Kevin SonnanburgInstitution: The University of Tennessee, KnoxvilleEmail: ksonnanb@vols.utk.edu

Abstract: Under mean curvature flow, a closed, embedded hypersurface M(t) becomes singular in finite time.For certain classes of mean-convex mean curvature flows, we show the continuity of the first singular time T andthe limit set “M(T )”, with respect to initial data. Although there are few local stability results, especially forthe sphere, little is known in terms of initial data. Where sophisticated energy methods fail, intuitive geometricarguments succeed. We employ an Angenent-like neckpinching argument to force singularities in nearby flows.However, since we cannot prescribe initial data, we combine Andrews α-non-collapsed condition and Colding andMinicozzis uniqueness of tangent flows to place appropriately sized spheres in the region inside the hypersurface.

84. Title: Blow-up problem for one dimensional fractional reaction diffusion equationSpeaker: Subhash SubediInstitution: University of Louisiana at LafayetteEmail: sxs2754@louisiana.edu

Abstract: We study the blow-up problems for ordinary caputo fractional differential equation and time depen-dent caputo-fractional reaction diffusion equation in one dimensional finite and infinite domain with a nonlinearsource. We also compare the solution with the solution of the standard reaction diffusion equation.

85. Title: Modeling Pharmacodynamics on HIV Latent InfectionSpeaker: Naveen K. Vaidya

Institution: San Diego State UniversityEmail: nvaidya@sdsu.edu

Abstract: While antiretroviral therapy has successfully controlled HIV replication in many patients, the phar-macodynamics of antiretroviral drugs can have impact on the treatment effectiveness. In this talk, I will presenta mathematical model of HIV latent infection dynamics that integrates the effects of drug pharmacodynamics.Using our model, we formulate a viral invasion threshold to establish the global stability of the infection-freesteady state and the viral persistence criteria. Our results highlight that success of treatment may be determinedby the choice of antiretroviral drugs in the treatment regimen.

86. Title: Modeling the Impact of Zika Virus Epidemic with VaccinationSpeaker: Wencel Valega-MackenzieInstitution: University of Tennessee, KnoxvilleEmail: wvalegam@vols.utk.eduCo-author(s): Karen Rios-Soto

Abstract: Zika virus (ZIKV) is a vector-borne disease that has rapidly spread during the year 2016 in morethan 50 countries around the world. The virus can cause severe birth defects and brain damage in babies if awoman is infected during pregnancy. As an intervention for controling the spread of the disease we study the costof a vaccination campaign to prevent new Zika infections in the near future. Although there is no formal vaccinefor ZIKV, The National Institute of Allergy and Infectious Diseases part of the National Institutes of Health haslaunched a vaccine trial at the beginning of August 2016 to control ZIKV transmission. Thus, in this work, weformulate a vaccination model for Zika virus including direct transmission. We calculate the basic reproductionnumber of the model to analyze the impact of vaccination including, perfect and imperfect vaccination. Weillustrate several numerical examples of the vaccination model to validate our theoretical results.

87. Title: The fundamental properties of a family of stochastic epidemic dynamic models for vector-borne diseases,Case study: malariaSpeaker: Divine WandukuInstitution: Georgia Southern UniversityEmail: dwanduku@georgiasouthern.edu

Abstract: A family of stochastic and deterministic SEIRS epidemic dynamic models for vector-borne diseaseis presented. The general nonlinear incidence rate of the disease determines the family type of the dynamicmodels. Furthermore, the family of epidemic models exhibits three random delays: - two of the delays representthe incubation periods of the disease inside the vector and human hosts, whereas the third delay is the periodof effective natural immunity against the disease. For the stochastic models, it is assumed that the diseasedynamic is influenced by random environmental fluctuations in the disease transmission and natural death ratesof humans which are represented by independent white noise processes. Thus, the stochastic disease dynamic is asystem of Ito-Doob stochastic differential equations, whereas the deterministic dynamics is a system of ordinarydifferential equations. Insights about the effects of the delays and the noises on (1) disease eradication and (2)extinction of the disease from the system are gained via comparative analyses of the family of stochastic anddeterministic models, and further critical examination of the significance of the delays and intensities of thewhite noises in the system on (1) the existence and stability of equilibria, and (2) on the asymptotic behavior ofthe solutions of the systems near the equilibria of the systems. Numerical simulation results are presented.

88. Title: Existence of solutions for a nonlocal fractional boundary value problemSpeaker: Min WangInstitution: Rowan UniversityEmail: wangmin@rowan.eduCo-author(s): Zhen Gao

Abstract: In this talk, we consider a nonlinear fractional boundary value problem with nonlocal boundaryconditions. The associated Green’s function is constructed as a series of functions by the perturbation approach.Criteria for the existence of solutions are obtained based on it.

89. Title: Large time behavior in defective Fokker-Planck equationsSpeaker: Tobias WohrerInstitution: Vienna University of Technology

Email: tobias.woehrer@tuwien.ac.atCo-author(s): Anton Arnold, Amit Einav

Abstract: The Fokker-Planck equation is an important equation in mathematical analysis with roots in sta-tistical physics and probability. Mostly motivated by recent work of Arnold and Erb, we will discuss optimallong-time behavior for solutions to the hypocoercive Fokker-Planck equation with focus on a defective driftmatrix (i.e. lacking eigenvectors). In analogy to defective ODE systems, the true decay rate is not purely ex-ponential, but rather of the form (1 + t2n)e−µt. In order to gain sharp decay estimates, we make use of anew nonsymmetric hypercontractivity result, which allows us to take advantage of the geometric nature of theFokker-Planck operator in the L2 setting. This is joint work with Anton Arnold and Amit Einav.

90. Title: Is Allee Effect critical for tumor progression?Speaker: Jacy ZanussiInstitution: jtz2c@mtmail.mtsu.eduEmail: Middle Tennessee State University

Co-author(s): Hugh Matlock, J. Angela Murdock, Khem Poudel, Zachariah Sinkala

Abstract: Tumor cells develop different strategies to cope with changing microenvironmental conditions. Wewill focus on adaptive phenotypic switching. Based on recent evidence, our model assumes that each cell in atumor resides in either of two mutually exclusive states: proliferating or migrating. From a probabilistic modelof switching between these two phenotypes, we derive a two-dimensional prey-predator system of ODEs withAllee effect that link cellular phenotypes to disease progression. If cell migration is allowed to increase withlocal cell density, any tumor cell population will persist in time, irrespective of its initial size. On the contrary,if cell motility is assumed to decrease with respect to local cell density, any tumor population below a certainsize threshold will eventually extinguish, a fact usually termed as Allee effect in ecology. The model has severalpossible applications. For instance, it could be used to predict the rate of disease progression in an individualpatient, and to improve screening methods.

91. Title: Lp Asymptotic Behavior of Solutions to General Hyperbolic-Parabolic Systems of Balance Laws in MultiSpace DimensionsSpeaker: Yanni ZengInstitution: University of Alabama at BirminghamEmail: ynzeng@uab.edu

Abstract: We study time asymptotic behavior of solutions for a general system of hyperbolic-parabolic balancelaws in m space dimensions, m ≥ 2. The system has physical viscosity matrices. Besides, there is a lower orderterm to account for relaxation, damping or chemical reaction. The viscosity matrices and the Jacobian matrix ofthe lower order term are rank deficient. We study Cauchy problem around a constant equilibrium state. Undera set of reasonable assumptions, existence of solution global in time is established, and Lp decay rates (p ≥ 2) ofthe solution to the constant equilibrium state are obtained. We may further study the large time behavior of thesolution. We show that it is time-asymptotically approximated by the solution of the corresponding linear systemwith the same initial data. For p ≥ 2, optimal Lp convergence rates to the asymptotic solution are obtained.These rates are faster by (t+ 1)−1/2 (or (t+ 1)−1/2 ln(t+ 2) if m = 2) when comparing to the convergence ratesto the constant equilibrium state. Our results are general and apply to physical models such as gas flows withtranslational and vibrational non-equilibrium. The result on asymptotic behavior is new even for the specialcase of hyperbolic balance laws.

Summary of the 2017 SEARCDE Program

Saturday, October 711:00am – 6:00pm Registration (CL Atrium 1000)

12:45pm – 1:00pm Opening Remarks (SC 109)Marcus Davis, Associate Dean for Research of the College of Science and MathematicsSean F. Ellermeyer, Chair of the Department of Mathematics

1:00pm – 2:00pm Suzanne Lenhart: Modeling Infectious Diseases with Environmental TransmissionPlenary 1 Moderator: Sean F. Ellermeyer (SC 109)

2:00pm – 2:20pm Coffee Break (SL Atrium 1001)PARALLEL SESSIONS

Session 1A Session 1B Session 1C Session 1D Session 1E Session 1FRoom: CL 1003 CL 1008 CL 1010 SC 212 SC 213 SC 214

Moderator: P. Laval C. Browne I. Aslan D. Ramirez C. Collins L. Ritter2:20pm – 2:40pm V. Alexiades C. Browne I. Aslan D. Ramirez C. Collins L. Ritter2:40pm – 3:00pm H. Bhatt N. Vaidya D. Burton L. Hermi M. Fury S. Rengaswami3:00pm – 3:20pm S. Liao M. Elmas C. Edholm C. Buse, L.

NguyenD. Regmi H. Kankana-

malage3:20pm – 3:40pm R. Leander H. Gulbudak E. Numfor J. Gemmer C. Lorton Z. Shuai3:40pm – 3:55pm Coffee Break (SL Atrium 1001)

PARALLEL SESSIONS

Session 2A Session 2B Session 2C Session 2D Session 2E Session 2FRoom: CL 1003 CL 1008 CL 1010 SC 212 SC 213 SC 214

Moderator: X. Gong H. Joshi M. Islam M. Wang R. Sharma S. Ngai3:55pm – 4:15pm X. Gong H. Joshi M. Islam M. Wang R. Sharma S. Ngai4:15pm – 4:35pm N. Iraniparast J. Murdock S. Almuthaybiri E. Demirci R. Mickens S. Robinson4:35pm – 4:55pm S. Ai H. Matlock Z. Denton R. Dahal M. Hameed M. Rivas4:55pm – 5:15pm M. Noorman L. Hadji Y. Raffoul T. Wohrer I. Amirali F. Drullion5:20pm – 6:20pm Michael Li: Mathematical Models for Infectious Diseases with Nonlocal State Structures

Plenary 2 Moderator: Liancheng Wang (SC 109)

6:30pm – 8:30pm RECEPTION DINNER (University Room A, B, C)

Sunday, October 87:30am – 11:00am Registration (CL Atrium 1000)7:30am – 8:30am Light Breakfast and Coffee (SL Atrium 1001)8:30am – 9:30am Alfonso Castro: Critical Point Theory and Multiplicity of Solutions to Elliptic Boundary Value Problems

Plenary 3 Moderator: Dhruba Adhikari (SC 109)9:30am – 9:50am Coffee Break (SL Atrium 1001)

PARALLEL SESSIONS

Session 3A Session 3B Session 3C Session 3D Session 3E Session 3FRoom: CL 1003 CL 1008 CL 1010 SC 212 SC 213 SC 214

Moderator: Y. Shao Z. Sinkala Y. Chung L. Castle L. Kong S. Sadhu9:50am – 10:10am Y. Shao Z. Sinkala Y. Chung L. Castle L. Kong S. Sadhu10:10am – 10:30am S. Subedi K. Poudel B. Pineyro K. Sonnanburg J. Neugebauer D. Wanduku10:30am – 10:50am J. Navratil A. Olifer Q. Chen Y. Zeng D. Maroncelli J. Graef10:50am – 11:10am D. Guo O. Egbelowo J. Paullet S. Ravindran A. Ludu M. Lafcı11:10am – 11:30am Coffee Break (SL Atrium 1001)11:30am – 12:30pm Jerry L. Bona: Applications of Water Wave Theory in Oceanography and Coastal Engineering

Plenary 4 Moderator: John Graef (SC 109)12:30pm – 1:30pm Lunch (SL Atrium 1001)

PARALLEL SESSIONS

Session 4A Session 4B Session 4C Session 4D Session 4ERoom: CL 1003 CL 1008 CL 1010 SC 212 SC 213

Moderator: W. Ding K. Berry B. Pantha K. Acharya C. Kunkel1:30pm – 1:50pm W. Ding K. Berry B. Pantha K. Acharya C. Kunkel1:50pm – 2:10pm L. Corsi J. Zanussi T. Miyaoka E. Harrell II D. Benko2:10pm – 2:30pm A. FALADE W. Valega-

MackenzieY. Dib Y. Hu C. Okhio, L.

Crimm2:30pm – 2:50pm D. Mathebula J. Nanware S. Sarwar Z. Allali

2:50pm Closing Remarks (SC 109), Coffee Available (SL Atrium 1001)