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Stochastic generalised KPP equations

Published online by Cambridge University Press:  14 November 2011

I. M. Davies ,
A. Truman  and
H. Z. Zhao
I. M. Davies
Affiliation:
Department of Mathematics, University of Wales Swansea, Singleton Park, Swansea SA2 8PP, U.K.
A. Truman
Affiliation:
Department of Mathematics, University of Wales Swansea, Singleton Park, Swansea SA2 8PP, U.K.
H. Z. Zhao
Affiliation:
Department of Mathematics, University of Wales Swansea, Singleton Park, Swansea SA2 8PP, U.K.
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Abstract

We classify multiplicative white noise perturbations k(·) dw, of generalised KPP equations and their effects on deterministic approximate travelling wave solutions by the behaviour of , the solutions of the stochastic generalised KPP equations converge to deterministic approximate travelling waves and if

being an associated potential energy, Фs a solution of the corresponding classical mechanical equations of Newton, D being a certain domain in R1 × Rr then the white noise perturbations essentially destroy the wave structure and force the solutions to die down.

For the case

(suppose the existence of the limit) we show that there is a residual wave form but propagating at a different speed from that of the unperturbed equations. Numerical solutions are included and give good agreement with theoretical results.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 126 , Issue 5 , 1996 , pp. 957 - 983
Copyright
Copyright © Royal Society of Edinburgh 1996

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