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

A. C. BRIOZZO - M. F. NATALE - D. A. TARZIA

JOURNAL OF NONLINEAR ANALYSIS

Elsevier

Año: 2007 vol. 67 p. 1989 - 1998

0362-546X

The mathematical analysis of a one-phase Lamé-Clapeyron-Stefan problem with nonlinear thermal coefficients following G. A. Tirskii, Soviet Physics Doklady, 4 (1959), 288-292 is obtained. Two related cases are considered, one of them has a temperature condition on the fixed face $x=0$ and the other one has a flux condition of the type $-q_{0}/sqrt{t}$ $left(q_{0}>0 ight)$. 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.