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Explicit solutions for a one-phase Stefan problem with temperature-dependent thermal conductivity

María F. Natale; Domingo A. Tarzia — 2006

Bollettino dell'Unione Matematica Italiana

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 $-q_{0}/\sqrt{t}$ ( $q_{0}>0$ ) at the fixed face $x=0$ . We obtain in both cases sufficient conditions for data in order to have a parametric representation of the solution of the similarity type for $t\geq t_{0}>0$ with $t_{0}$ an arbitrary positive time. These explicit solutions are obtained through the unique solution of an integral equation with the time as a parameter....

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