Singular limit of a transmission problem for the parabolic phase-field model

Giulio Schimperna

Applications of Mathematics (2000)

  • Volume: 45, Issue: 3, page 217-238
  • ISSN: 0862-7940

Abstract

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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.

How to cite

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Schimperna, Giulio. "Singular limit of a transmission problem for the parabolic phase-field model." Applications of Mathematics 45.3 (2000): 217-238. <http://eudml.org/doc/33056>.

@article{Schimperna2000,
abstract = {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.},
author = {Schimperna, Giulio},
journal = {Applications of Mathematics},
keywords = {phase-field models; maximal monotone operators; transmission problems; parabolic PDEs; phase-field models; maximal monotone operators; transmission problems; parabolic equations; singular transition},
language = {eng},
number = {3},
pages = {217-238},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Singular limit of a transmission problem for the parabolic phase-field model},
url = {http://eudml.org/doc/33056},
volume = {45},
year = {2000},
}

TY - JOUR
AU - Schimperna, Giulio
TI - Singular limit of a transmission problem for the parabolic phase-field model
JO - Applications of Mathematics
PY - 2000
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 45
IS - 3
SP - 217
EP - 238
AB - 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.
LA - eng
KW - phase-field models; maximal monotone operators; transmission problems; parabolic PDEs; phase-field models; maximal monotone operators; transmission problems; parabolic equations; singular transition
UR - http://eudml.org/doc/33056
ER -

References

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