An integral equation in order to solve a one-phase Stefan problem with nonlinear thermal conductivity

M.F. NATALE – D.A. TARZIA

Rosario

Jornada; Primeras Jornadas Sobre Ecuaciones Diferenciales, Optimización y Análisis Numérico; 2004

Universidad Austral

We study a one-phase Stefan problem for a semi-infinite material with temperature-dependent thermal conductivity with a constant temperature or a heat flux condition of the type }$-q_{0}/sqrt{t}$ $left( q_{0}>0 ight) $ { m at the fixed face }$x=0$. { m We obtain in both cases sufficient conditions for data in order to have a parametric representation of the solution of the similarity type for }$tgeq t_{0}>0$ { m with} $t_{0}$ { m % an arbitrary positive time. These explicit solutions are obtained through the unique solution of an integral equation with the time as a parameter.