The Stefan problem with temperature-dependent thermal conductivity and aconvective term with a convective condition at the fixed face

Adriana C. Briozzo; María F. Natale; Domingo A. Tarzia

doi:10.3934/cpaa.2010.9.1209

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2010, Volume 9, Issue 5: 1209-1220. Doi: 10.3934/cpaa.2010.9.1209

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The Stefan problem with temperature-dependent thermal conductivity and a convective term with a convective condition at the fixed face

1.
Depto. de Matemática and CONICET, FCE, Universidad Austral, Paraguay 1950, S2000FZF Rosario
2.
Depto. de Matemática , FCE, Universidad Austral, Paraguay 1950, S2000FZF Rosario

Received: July 31, 2009

Revised: August 31, 2009

Published: August 2010

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Abstract

We study a one-phase Stefan problem for a semi-infinite material with temperature-dependent thermal conductivity and a convective term with a convective boundary condition at the fixed face $x=0$. We obtain 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. We obtain explicit solutions through the unique solution of a Cauchy problem with the time as a parameter and we also give an algorithm in order to compute the explicit solution.

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Mathematics Subject Classification: Primary: 35R35, 80A22, 35C05.

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