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

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