Exact solutions in non-linear diffusion
Michael J. South · ThinkTech (Texas Tech University) · 1995
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 \ {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.