Journal of Convex Analysis 06 (1999), No. 1, 041--058
Copyright Heldermann Verlag 1999
Asymptotic Analysis to a Phase-Field Model with a Nonsmooth Memory Kernel
Giovanna Bonfanti
Dip. di Elettronica per l'Automazione, Università di Brescia, Via Branze 38, 25123 Brescia, Italy
Fabio Luterotti
Dip. di Elettronica per l'Automazione, Università di Brescia, Via Branze 38, 25123 Brescia, Italy
A phase-field model based on the Gurtin-Pipkin heat flux law is considered. The resulting system has been investigated by Colli and Lauren\c cot who proved existence and uniqueness results, when the time relaxation coefficient is strictly positive. The aim of this paper is the study of the asymptotic behaviour of such a solution, as the time relaxation goes to zero, and of the related limit problem.
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