J Austral Math Soc Ser B 37 pp458--473, 1996.

Reaction waves and non-constant diffusivities

S. D. Watt and R. O. Weber

(Received 18 October 1993; revised April 1994)

Abstract

A reaction-diffusion equation with non-constant diffusivity,

ut = (D(x, t )ux )x + F(u )

is studied for D(x, t ) a continuous function. The conditions under which the equation can be reduced to an equivalent constant diffusion equation are derived. Some exact forms for D(x, t ) are given. For D(x, t ) a stochastic function, an explicit finite difference method is used to numerically determine the effect of randomness in D(x, t ) upon the speed of the reaction wave solution to Fisher's equation. The extension to two spatial dimensions is considered.

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Authors

S. D. Watt
Ind. and App. Maths, Tamaki Campus, University of Auckland, Auckland, N.Z.
R. O. Weber
Dept of Maths, University of NSW, Australian Defence Force Academy, Canberra, Australia.

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