Geodesic
Singular limit of a transmission problem for the parabolic phase-field model
Applications of Mathematics, Tome 45 (2000) no. 3, pp. 217-238 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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.
DOI : 10.1023/A:1023070928404
Classification : 35B40, 35K55, 80A22
Keywords: phase-field models; maximal monotone operators; transmission problems; parabolic PDEs 
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Schimperna, Giulio. Singular limit of a transmission problem for the parabolic phase-field model. Applications of Mathematics, Tome 45 (2000) no. 3, pp. 217-238. doi: 10.1023/A:1023070928404

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