Abstract
Change of phase problems with space-dependent melting temperature are considered. A weak formulation is given, pointing out that relevant differences occur with respect to the case of constant melting temperature. Next, analyzing the case in which weak solutions are suitably smooth, it is found that (i) mushy regions may appear even if volumetric heat sources are absent; (ii) a differential system is satisfied, consisting of parabolic equations and first order hyperbolic equations coupled through free boundaries; (iii) the interface conditions have the form of “unilateral constraints”. Finally, a model problem is studied and the existence of a smooth solution is proved.
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