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The travelling wave fronts of nonlinear reaction–diffusion systems via Friedlin's stochastic approaches

Published online by Cambridge University Press:  14 November 2011

Huaizhong Zhao
Huaizhong Zhao
Affiliation:
Mathematics Institute, University of Warwick, Coventry CV4 7AL, England, U.K.
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Abstract

In this paper we study the asymptotic behaviour of reaction–diffusion systems with a small parameter by using the n-dimensional Feynman–Kac formula and large deviation theory. The generalised solutions are introduced in Section 2. We obtain the travelling wave joining an unstable steady state and an asymptotically stable steady state of a diffusionless dynamical system in a reaction–diffusion system with nonlinear ergodic interactions, and a special case with nonlinear reducible interactions.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 124 , Issue 2 , 1994 , pp. 273 - 299
Copyright
Copyright © Royal Society of Edinburgh 1994

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