Tel-Aviv University
School of Mathematical Sciences
Department Colloquium
Monday, December 1, 2014
Schreiber 006, 12:15
Henri Berestycki
Ecoles des hautes études en sciences sociales
Propagation in non homogeneous media and applications
Abstract: The classical theory of the Fisher and Kolmogorov-Petrovsky-Piskunov equation derives the spreading properties for a reaction-diffusion equation in a homogeneous setting. A well known invasion speed governs the asymptotic speed of propagation. This equation plays an important role in a variety of contexts in ecology, biology and physics. In this talk, I will first introduce reaction-diffusion equations, and describe some of their motivations as well as the underlying mechanism. I will then review the classical theory for homogeneous Fisher-KPP equations.
In applications, one often wishes to understand the effects of heterogeneity. This leads to challenging mathematical questions and I will describe some of them. I will then discuss more in detail the effect of inclusion of a line with fast diffusion on biological invasions in the plane. I will report on recent results on this question.
