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Long time convergence for a class of variational phase-field models

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  • In this paper we analyze a class of phase field models for the dynamics of phase transitions which extend the well-known Caginalp and Penrose-Fife phase field models. We prove the existence and uniqueness of the solution of a corresponding initial boundary value problem and deduce further regularity of the solution by exploiting the so-called regularizing effect. Finally we study the long time behavior of the solution and show that it converges algebraically fast to a stationary solution as $t$ tends to infinity.
    Mathematics Subject Classification: Primary: 35B40, 35K45; Secondary: 80A22.

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