Special Session 8: Propagation Phenomena in Reaction-Diffusion Systems

On the stability and behavior of solutions of the Allen-Cahn-Nagumo equation

Toru Kan
Osaka Metropolitan University
Japan
Co-Author(s):    
Abstract:
We consider the Allen-Cahn-Nagumo equation in the whole plane. It is known that V-shaped travelling wave solutions exist and are stable under perturbations decaying at infinity. In this talk, we first consider conditions for a solution to converge to a V-shaped travelling wave solution, and then discuss the asymptotic behavior of solutions whose initial values are close to indicator functions with noncompact support.