On a nonlinear moving boundary problem with heterogeneity: Application of a reciprocal transformation (Q1113025)

In recent work it has been shown that a reciprocal transformation may be used to obtain a parametric representation of the solution to an important class of nonlinear moving boundary problems. Here, use is made of a result due to Broadbridge to incorporate a degree of heterogeneity into the class of nonlinear media for which the solution may be constructed. The nonlinear transport equation in the posed boundary value problem is of a type that arises as an evaporation model in soil mechanics. The exact solution obtained representes an extension of the classical Neumann solution.