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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