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

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

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