Abstract
In this paper we study an initial-boundary value Stefan-type problem with phase relaxation where the heat flux is proportional to the gradient of the inverse absolute temperature. This problem arise naturally as limiting case of the Penrose-Fife model for diffusive phase transitions with nonconserved order parameter if the coefficient of the interfacial energy is taken as zero. It is shown that the relaxed Stefan problem admits a weak solution which is obtained as limit of solutions to the Penrose-Fife phase-field equations. For a special boundary condition involving the heat exchange with the surrounding medium, also uniqueness of the solution is proved.
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Colli, P., Sprekels, J. On a Penrose-Fife model with zero interfacial energy leading to a phase-field system of relaxed Stefan type. Annali di Matematica pura ed applicata 169, 269–289 (1995). https://doi.org/10.1007/BF01759357
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DOI: https://doi.org/10.1007/BF01759357