Istituto di Matematica Applicata e Tecnologie Informatiche     
Schimperna G. Singular limit of a transmission problem for the parabolic phase-field model. Preprint ercim.cnr.ian//1999-1134, 1999.
A transmission problem describing the thermal interchange between two regions occupied by possibly different fluids, which may present phase transitions, is studied in the framework of the Caginalp-Fix phase field model. Dirichlet (or Neumann) and Cauchy conditions are required. A regular solution is obtained by means of approximation techniques for parabolic systems. Then, an asymptotic study of the problem is carried out as the time relaxation parameter for the phase field tends to 0 in one of the domains. It is also proved that the limit formulation admits a unique solution in a suitable weak sense.
Subject Phase-field models, maximal monotone operators, transmission problems, parabolic PDEs
35B40, 35K55, 80A22

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