Spreading speeds for reaction-diffusion equations in unbounded domains

A fundamental feature which accounted for the success of reaction-diffusion equations is the description of spreading phenomena in unbounded domains. Estimating the asymptotic spreading speeds of solutions whose initial conditions are given is indeed one of the most important aspects from a theoretical point of view as well as in all sorts of applications in biology and ecology. In the talk, I will report on various definitions and estimates of the spreading speeds of solutions of some reaction-diffusion equations in very general domains with obstacles, or for a general class of initial conditions.

The talk is based on some joint works with H. Berestycki, N. Nadirashvili and Y. Sire.