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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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