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On a conserved Penrose-Fife type system. (English) Zbl 1099.35022

Summary: We deal with a class of Penrose-Fife type phase field models for phase transitions, where the phase dynamics is ruled by a Cahn-Hilliard type equation. Suitable assumptions on the behaviour of the heat flux as the absolute temperature tends to zero and to \(+\infty \) are considered. An existence result is obtained by a double approximation procedure and compactness methods. Moreover, uniqueness and regularity results are proved as well.

MSC:

35G30 Boundary value problems for nonlinear higher-order PDEs
35D05 Existence of generalized solutions of PDE (MSC2000)
35B45 A priori estimates in context of PDEs
80A22 Stefan problems, phase changes, etc.
35B40 Asymptotic behavior of solutions to PDEs
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References:

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