# Delayed reaction-diffusion PDE coupled to difference equation

On Monday March 6th at 11:00am, Prof. Abdennasser CHEKROUN will give a seminar in the Department of Mathematics Conference Room, Rm. 1S-213.

ABSTRACT:

We consider a class of biological models represented by a system composed of reaction-diffusion PDE

coupled with difference equations (renewal equations) in n-dimensional space, with nonlocal dispersal

terms and implicit time delays. The difference equation generally arises, by means of the method of

characteristics, from an age-structured partial differential system. Using upper and lower solutions,

we study the existence of monotonic planar traveling wave fronts connecting the extinction state to the

uniform positive state. The corresponding minimum wave speed is also obtained. In addition,

we investigate the effect of the parameters on this minimum wave speed and we give a detailed analysis of

its asymptotic behavior. Before all of that, for the presentation to be suitable for the unfamiliar but

also for young researchers with these notions, I would like to introduce the concept of traveling waves

by using more basic equations.

Abdennasser Chekroun is a mathematician specializing in delayed differential equations and conducts

research on cell modeling and the modeling of certain epidemiological phenomena. Abdennasser CHEKROUN

studied mathematics at the University of Tlemcen (Algeria) and obtained a doctorate from the

University of Claude Bernard Lyon 1 (France) in 2016. He is currently a professor at the

University of Tlemcen and a member of the research laboratory in Non-Linear Analysis and

Applied Mathematics (Tlemcen). Abdennasser CHEKROUN's research focuses on analysis, dynamic systems,

and applications. His main research themes are delay differential equations, reaction-diffusion equations

with delay and traveling wavefronts, and mathematical modeling. He is also the first winner of the Audin

chair of the Insmi (National Institute of Mathematical Sciences and their interactions) in 2020.