On travelling waves for the stochastic Fisher-Kolmogorov-Petrovsky-Piscunov equation

Abstract

This paper is concerned with properties of the wave speed for the stochastically perturbed Fisher-Kolmogorov-Petrovsky-Piscunov (FKPP) equation. It was shown in the classical 1937 paper by Kolmogorov, Petrovsky and Piscunov that the large time behavior of the solution to the FKPP equation with Heaviside initial data is a travelling wave. In a seminal 1995 paper Mueller and Sowers proved that this also holds for a stochastically perturbed FKPP equation. The wave speed depends on the strength σ of the noise. In this paper bounds on the asymptotic behavior of the wave speed c(σ) as σ→0 and σ→∞ are obtained. © 2005 Springer Science+Business Media, Inc.