Proceedings of the Royal Society of Edinburgh: Section A Mathematics

Research Article

Travelling-waves for the FKPP equation via probabilistic arguments

Simon C. Harrisa1

a1 Department of Mathematical Sciences, University of Bath, Bath BA2 7AY, UK

Abstract

We outline a completely probabilistic study of travelling-wave solutions of the FKPP reaction-diffusion equation that are monotone and connect 0 to 1. The necessary asymptotics of such travelling-waves are proved using martingale and Brownian motion techniques. Recalling the connection between the FKPP equation and branching Brownian motion through the work of McKean and Neveu, we show how the necessary asymptotics and results about branching Brownian motion combine to give the existence and uniqueness of travelling waves of all speeds greater than or equal to the critical speed.

(Received August 18 1997)

(Accepted April 16 1998)