Exact solutions in non-linear diffusion

Date

1995-05

Journal Title

Journal ISSN

Volume Title

Publisher

Texas Tech University

Abstract

The nonlinear diffusion equation, {w{u)ux)x — Ut, has application in many areas of science and technology. We discuss exact solutions of this equation for three weight functions-w"^, e", and \n{u). We obtain these solutions in each case by "inverting the weight function," that is, we make the substitution v = w{u) and solve the resulting equation for v. Although we do not use similarity techniques, most of our solutions turn out to be similarity solutions-a brief look at similarity methods is presented. The solution we find for ln{u) appears not to have been published.

Description

Keywords

Partial, Diffusion processes, Differential equations

Citation