By using Lie group methods, an analysis was made of a non-linear diffusion equation for an inhomogeneous medium: f(x)ut = [g(x)D(u)ux]x, where D(u) was an arbitrary diffusion coefficient and f(x) and f(x) were arbitrary thermal coefficients. Such an equation had a wide range of applications. The use of a Lie group similarity method led to a classification of the diffusion and thermal coefficients in terms of symmetry properties. By means of the adjoint representation, an optimum system of similarity reductions was obtained. Exact similarity solutions of the second-order ordinary differential equations which resulted from the reductions were illustrated by means of examples.

E.A.Saied: Journal of the Physical Society of Japan, 1995, 64[4], 1092-7