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A nonlinear supercooled Stefan problem

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Abstract

We study the supercooled one-phase Stefan problem for a semi-infinite material with temperature-dependent thermal conductivity at the fixed face \(x=0\). We obtain sufficient conditions for data in order to have existence of a solution of similarity type, local in time and finite-time blow-up occurs. This explicit solution is obtained through the unique solution of an integral equation with the time as a parameter.

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Authors and Affiliations

  1. CONICET, F.C.E., Depto. de Matemática, Univ. Austral, Paraguay 1950, S2000FZF, Rosario, Argentina

    Adriana C. Briozzo & Maria F. Natale

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  1. Adriana C. Briozzo
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  2. Maria F. Natale
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Correspondence to Adriana C. Briozzo.

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Briozzo, A.C., Natale, M.F. A nonlinear supercooled Stefan problem. Z. Angew. Math. Phys. 68, 46 (2017). https://doi.org/10.1007/s00033-017-0788-6

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  • DOI: https://doi.org/10.1007/s00033-017-0788-6

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