Travelling fronts and entire solutions of the Fisher-KPP equation in RN

This paper is devoted to time-global solutions of the Fisher-KPP equation in R-N : u(1) = Deltau + f(u), 0 < u(x, t) < 1, x is an element of R-N, t is an element of R 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 acid radial solutions. Furthermore, up to an additional assumption, a given solution u can be represented in terms of such a mixing of travelling fronts.