J Austral Math Soc Ser B 33 pp321--349, 1992.

Local transformations between some nonlinear diffusion equations

J. R. King

Abstract

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.

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Author

J. R. King

Dept. of Theoretical Mathematics, University of Nottingham, Nottingham, NG7 2RD, U.K.