Existence of an exact solution for a one-phase Stefan problem with nonlinear thermal coefficients from Tirskii’s method Original Research Article

The mathematical analysis of a one-phase Lamé–Clapeyron–Stefan problem with nonlinear thermal coefficients following [G.A. Tirskii, Two exact solutions of Stefan’s nonlinear problem, Sov. Phys. Dokl. 4 (1959) 288–292] is obtained. Two related cases are considered; one of them has a temperature condition on the fixed face x=0x=0 and the other one has a flux condition of the type View the MathML source−q0/t(q0>0). We obtain in both cases sufficient conditions for data in order to have the existence of an explicit solution of a similarity type which is given by using a double fixed point.