Istituto di Matematica Applicata e Tecnologie Informatiche     
Rossi R. Asymptotic Analysis of the Caginalp Phase-Field Model for two Vanishing Time Relaxation Parameters. Preprint ercim.cnr.ian//2002-1293, 2002.
This paper addresses the Caginalp conserved phase-field system, which couples an energy balance equation containing a time relaxation parameter $varepsilon>0$ and a source term f, with a Cahn-Allen type dynamics for the order parameter. The analysis is focused on the asymptotic behaviour of the solutions of this parabolic system firstly as $varepsilon downarrow 0$, and secondly as both $varepsilon$ and the coefficient $delta>0$ of the interfacial energy term in the equation for the order parameter tend to zero. The limit equations are the viscous Cahn-Hilliard equation with source term in the former case, and the Cahn-Hilliard equation with source in the latter one. Convergence results are proved, yielding the existence of solutions for both problems, while uniqueness follows from continuous dependence on the data; error estimates are obtained as well. An analogous asymptotic analysis is carried out for the viscous Cahn-Hilliard equation as $delta downarrow 0$.
Subject Phase-field system, relaxation parameters, Cahn-Hilliard equation

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