Group Transformations and the Nonlinear Heat Diffusion Equation

Abstract

A nonlinear diffusion equation with a power law diffusion coefficient is studied. Self-similar and partially invariant solutions are shown to be identical. The theory of homology is introduced and used to generate classes of equations, the solutions of which are related through Backlund transformations. An example of an application is given, which generalizes the solution of Storm (J. Appl. Phys., 22 (1951) pp. 940–951) on heat conduction in metals.