On a class of reciprocal Stefan moving boundary problems

Abstract

This paper concerns the action of reciprocal transformations on a class of moving boundary problems of Stefan type. Thus, an established integral representation is combined with a reciprocal transformation to obtain parametric exact solution to classes of moving boundary problems which arise, in particular, in the context of the percolation of liquids through a porous medium such as soil. Importantly, the procedure is shown to extend to a wide class of moving boundary value problems which incorporate heterogeneity in the porous medium.