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Reaction waves and non-constant diffusivities

Published online by Cambridge University Press:  17 February 2009

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

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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.

Type
Research Article
Information
The ANZIAM Journal , Volume 37 , Issue 4 , April 1996 , pp. 458 - 473
Copyright
Copyright © Australian Mathematical Society 1996

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