Singular limit of a transmission problem for the parabolic phase-field model
Applications of Mathematics, Tome 45 (2000) no. 3, pp. 217-238
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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.
DOI :
10.1023/A:1023070928404
Classification :
35B40, 35K55, 80A22
Keywords: phase-field models; maximal monotone operators; transmission problems; parabolic PDEs
Keywords: phase-field models; maximal monotone operators; transmission problems; parabolic PDEs
@article{10_1023_A_1023070928404, author = {Schimperna, Giulio}, title = {Singular limit of a transmission problem for the parabolic phase-field model}, journal = {Applications of Mathematics}, pages = {217--238}, publisher = {mathdoc}, volume = {45}, number = {3}, year = {2000}, doi = {10.1023/A:1023070928404}, mrnumber = {1757242}, zbl = {1058.35041}, language = {en}, url = {http://geodesic.mathdoc.fr/articles/10.1023/A:1023070928404/} }
TY - JOUR AU - Schimperna, Giulio TI - Singular limit of a transmission problem for the parabolic phase-field model JO - Applications of Mathematics PY - 2000 SP - 217 EP - 238 VL - 45 IS - 3 PB - mathdoc UR - http://geodesic.mathdoc.fr/articles/10.1023/A:1023070928404/ DO - 10.1023/A:1023070928404 LA - en ID - 10_1023_A_1023070928404 ER -
%0 Journal Article %A Schimperna, Giulio %T Singular limit of a transmission problem for the parabolic phase-field model %J Applications of Mathematics %D 2000 %P 217-238 %V 45 %N 3 %I mathdoc %U http://geodesic.mathdoc.fr/articles/10.1023/A:1023070928404/ %R 10.1023/A:1023070928404 %G en %F 10_1023_A_1023070928404
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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