A similarity solution to a nonlinear diffusion equation of the singular type: a uniformly valid solution by perturbations

Abstract

The one-dimensional nonlinear diffusion equation is solved by a perturbation technique. It is assumed that the diffusivity varies as a nonnegative power of the concentration, while the concentration at the supply surface varies as another power of time. The resulting similarity solution that has been derived via a perturbation scheme remains valid for all times and all distances. Explicit series formulae are also derived for the location of the concentration front. Since diffusivity vanishes at zero concentration, the study here pertains to a singular problem.