Istituto di Matematica Applicata e Tecnologie Informatiche     
Bonetti E. Some asymptotic analysis for hyperbolic relaxed Stefan problems with memory. Preprint ercim.cnr.ian//1998-1100, 1998.
This paper is devoted to the study of some diffusive phase transition problems in materials with memory, in the spirit of the theory of Gurtin and Pipkin, which leads to a hyperbolic integrodifferential energy equation. We prove existence and uniqueness of the solution to the phase-field problem with zero time relaxation. At the same time, we examine some asymptotic relations with the complete phase-field problem and the hyperbolic relaxed Stefan problem with memory. Moreover, we show that the solution of the latter problem can be considered as the limit of the solution of the related phase-field problem as the relaxation parameter (yielding the thermal dissipation) approaches zero. The procedure we have used is based on a priori estimates together with some compactness and monotonicity arguments, allowing us to pass to the limit.
Subject Diffusive phase transition problems

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