Travelling-waves for the FKPP equation via probabilistic arguments
- 1 January 1999
- journal article
- Published by Cambridge University Press (CUP) in Proceedings of the Royal Society of Edinburgh: Section A Mathematics
- Vol. 129 (3) , 503-517
- https://doi.org/10.1017/s030821050002148x
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.This publication has 15 references indexed in Scilit:
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