One-phase Stefan problem with temperature-dependent thermal conductivity and a boundary condition of Robin type

Abstract

We study a one-phase Stefan problem for a semi-in nite material with temperature-dependent thermal conductivity with a boundary condition of Robin type at the xed face x = 0. We obtain su cient conditions for data in order to have a parametric representation of the solution of similarity type for t ≥ t0 > 0 with t0 an arbitrary positive time. This explicit solution is obtained through the unique solution of an integral equation with the time as a parameter.