FREE-BOUNDARY PROBLEMS WITH NONLINEAR DIFFUSION

It is shown that whenever a nonlinear diffusion model can be solved on a semi-infinite domain, with the standard boundary conditions of constant concentration, then the same model can be adjusted to yield exact solutions to free boundary problems. This is true not only for those diffusion equations that can be solved directly, but also for the special models obtainable via Philip's inverse method. New solutions are developed for two practical free boundary problems. The first represents solidification over a mould with dissimilar nonlinear thermal properties and the second represents saturated/unsaturated absorption in the soil beneath a pond.