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.

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.