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Local transformations between some nonlinear diffusion equations

Published online by Cambridge University Press:  17 February 2009

J. R. King
J. R. King
Affiliation:
Dept. of Theoretical Mechanics, University of Nottingham, Nottingham, NG7 2RD, U.K.
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Abstract

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We derive local transformations mapping radially symmetric nonlinear diffusion equations with power law or exponential diffusivities into themselves or into other equations of a similar form. Both discrete and continuous transformations are considered. For the cases in which a continuous transformation exists, many additional forms of group-invariant solution may be constructed; some of these solutions may be written in closed form. Related invariance properties of some multidimensional diffusion equations are also exploited.

Type
Research Article
Information
The ANZIAM Journal , Volume 33 , Issue 3 , January 1992 , pp. 321 - 349
Copyright
Copyright © Australian Mathematical Society 1992

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