Travelling Fronts and Entire Solutions¶of the Fisher-KPP Equation in ℝN

Abstract:

This paper is devoted to time-global solutions of the Fisher-KPP equation in ℝ^N:

where f is a C ² concave function on [0,1] such that f(0)=f(1)=0 and f>0 on (0,1). It is well known that this equation admits a finite-dimensional manifold of planar travelling-fronts solutions. By considering the mixing of any density of travelling fronts, we prove the existence of an infinite-dimensional manifold of solutions. In particular, there are infinite-dimensional manifolds of (nonplanar) travelling fronts and radial solutions. Furthermore, up to an additional assumption, a given solution u can be represented in terms of such a mixing of travelling fronts.