Existence of multi-dimensional pulsating fronts for KPP equations: a new formulation approach

Abstract

This paper is concerned with the existence of pulsating travelling fronts for a KPP reaction-diffusion equation posed in a multi-dimensional periodic medium. We provide an alternative proof of the classic existence result. Our proof relies largely on the construction of a wave profile under a moving frame, which avoids many technical difficulties in dealing with degenerate elliptic equations. Intriguingly, our analysis also yields that the profile of the front propagating along each rational direction in $\mathbb{S}^{N-1}$ is periodic in time.