Special Session 6: Propagation dynamics of PDEs: recent progress and trends

Reaction-diffusion equations in R^N: convergence to fronts
Francois Hamel
Aix-Marseille University
France
Co-Author(s):    Hongjun Guo and Luca Rossi
Abstract:
This talk is concerned with reaction-diffusion-advection equations in homogeneous or spatially periodic media. I will discuss the asymptotic properties of the solutions of the Cauchy problem, under an assumption of weak stability of the constant steady states 0 and 1, or for Fisher-KPP reactions. I will especially show that front profiles appear, along sequences of times and points, in the large-time dynamics of the solutions, whether their initial supports be bounded or unbounded. I will also discuss further geometrical properties of the asymptotic invasion shapes of invading solutions. The talk is based on some joint works with Hongjun Guo and Luca Rossi.