Dissertation/Thesis Abstract

Long Time Behavior for Reaction-Diffusion Population Models
by Wu, Yixiang, Ph.D., University of Louisiana at Lafayette, 2015, 76; 10002390
Abstract (Summary)

In this work, we study the long time behavior of reaction-diffusion models arising from mathematical biology. First, we study a reaction-diffusion population model with time delay. We establish a comparison principle for coupled upper/lower solutions, prove the existence/uniqueness result for the model, and show the global asymptotic behavior of the model by constructing successive improved upper/lower solutions. Next, we consider a reaction-diffusion equation with continuous delay and spatial variable coefficients. We prove the global attractivity of the positive steady state by showing that the omega limit set is a singleton. Finally, we study an SIS reaction-diffusion model with spatial heterogeneous disease transmission and recovery rates. We define a basic reproduction number and obtain some existence and non-existence results of the endemic equilibrium of the model. We then study the global attractivity of the steady state for two special cases.

Indexing (document details)
Advisor: Deng, Keng
Commitee: Ackleh, Azmy, Ng, Ping Wong
School: University of Louisiana at Lafayette
Department: Sciences
School Location: United States -- Louisiana
Source: DAI-B 77/06(E), Dissertation Abstracts International
Subjects: Mathematics
Keywords: Asymptotic behavior, Population models, Reaction-diffusion equations
Publication Number: 10002390
ISBN: 9781339419008