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Large time behaviour of solutions to Penrose-Fife phase change models. (English) Zbl 1079.35021

Summary: A non-conserved phase transition model of Penrose-Fife type is considered where Dirichlet boundary conditions for the temperature are taken. A sketch of the proof of existence and uniqueness of the solution is given. Then, the large time behaviour of such a solution is studied. By using the Simon-Łojasiewicz inequality it is shown that the whole solution trajectory converges to a single stationary state. Due to the noncoercive character of the energy functional, the main difficulty in the proof is to control the large values of the temperature. This is achieved by means of nonstandard a priori estimates.

MSC:

35B40 Asymptotic behavior of solutions to PDEs
80A22 Stefan problems, phase changes, etc.
35K50 Systems of parabolic equations, boundary value problems (MSC2000)
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