Istituto di Matematica Applicata e Tecnologie Informatiche     
Schimperna G. Some convergence results for a class of nonlinear phase-field evolution equations. Preprint ercim.cnr.ian//1999-1135, 1999.
Two heat diffusion problems in the framework of the parabolic phase-field model are presented, the first related to a single isotropic fluid and the other describing the heat transmission between two regions occupied by different substances; some existence and uniqueness results are briefly recalled. Then, an asymptotic study of the problems is carried out as the phase-field equation collapses to an energy balance relation of Stefan type, in the first case in the whole domain, and in the second in only one of the considered regions. In both cases, a convergence result for the solutions is proved; particularly interesting seems the transmission case, where, in order to avoid the arising of compatibility conditions at the interface, it has been necessary to rewrite the problem in terms of graph convergence of abstract maximal monotone operators.
Subject Phase-field models, abstract subdifferential operators, evolution equations, graph convergence
35B40, 35K45, 35K55, 35R35, 80A22

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