Journal of Statistical Physics

, Volume 120, Issue 3, pp 421–477

On Travelling Waves for the Stochastic Fisher–Kolmogorov–Petrovsky–Piscunov Equation

Article

DOI: 10.1007/s10955-005-5960-2

Cite this article as:
Conlon, J.G. & Doering, C.R. J Stat Phys (2005) 120: 421. doi:10.1007/s10955-005-5960-2

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.

Key words

Stochastic pdecontact processparticle systems

Copyright information

© Springer Science+Business Media, Inc. 2005

Authors and Affiliations

  1. 1.Department of Mathematics and Michigan Center for Theoretical PhysicsUniversity of MichiganAnn Arbor