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Positivity of the temperature for phase transitions with micro-movements. (English) Zbl 1116.80015
In this paper the thermodynamic consistency of a class of solid liquid phase transition models proposed by Fremond is studied. The derivation of the model based on the two scale, micro and macro, modeling is reviewed in some detail. The thermodynamic consistency of these models is proved to be equivalent with the temperature positively. Under rater weak assumptions on the data it is proved that the temperature is separated uniformly by zero almost everywhere. The proof is based on a uniform bound for the inverse temperature. The result is quite general and may be applied to all dissipative models of that type.

80A22 Stefan problems, phase changes, etc.
35B50 Maximum principles in context of PDEs
Full Text: DOI
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