Convergence of phase field to phase relaxation models governed by an entropy equation with memory
Articolo
Data di Pubblicazione:
2006
Citazione:
Convergence of phase field to phase relaxation models governed by an entropy equation with memory / G. Gilardi, E. Rocca. - In: MATHEMATICAL METHODS IN THE APPLIED SCIENCES. - ISSN 0170-4214. - 29:18(2006), pp. 2149-2179. [10.1002/mma.765]
Abstract:
The subject of the present paper consists in proving the convergence of a phase-field model, based on the entropy equation with memory, to phase relaxation. The well-posedness and the long-time behaviour of solutions for the non-linear and singular phase-field system have been recently shown by Bonetti et al. (Preprint IMATI-CNR, 2005; Discrete Contin. Dyn. Syst. Ser B, in press). Here, we study the asymptotic behaviour of such solutions as the interfacial energy coefficient tends to zero. The limit problem is a phase relaxation problem with memory, which is new. We prove well-posedness results through convergence under rather general assumptions. However, the case of a quadratic non-linearity for the latent heat is excluded. Such a situation is dealt for the problem without memory in a generalized setting by introducing an ad hoc logarithm. Copyright (c) 2006 John Wiley & Sons, Ltd.
Tipologia IRIS:
01 - Articolo su periodico
Keywords:
phase transitions; phase relaxation; asymptotic analysis; non-linear and singular system; continuous dependence; a priori estimates
Elenco autori:
G. Gilardi, E. Rocca
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