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Long time convergence for a class of variational phase-field models. (English) Zbl 1178.35065

Summary: 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.

MSC:

35B40 Asymptotic behavior of solutions to PDEs
80A22 Stefan problems, phase changes, etc.
35K51 Initial-boundary value problems for second-order parabolic systems
35K55 Nonlinear parabolic equations
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