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Weak solution to a phase‐field transmission problem in a concentrated capacity
Author(s) -
Schimperna Giulio
Publication year - 1999
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/(sici)1099-1476(19990925)22:14<1235::aid-mma82>3.0.co;2-w
Subject(s) - mathematics , uniqueness , regularization (linguistics) , heat equation , mathematical analysis , neighbourhood (mathematics) , galerkin method , heat capacity , thermodynamics , finite element method , computer science , physics , artificial intelligence
The heat diffusion in a fluid with possible phase change is studied as the boundary condition in a part Γ of the edge of the considered region consists in another diffusion equation for the traces of the unknowns. This feature, called concentrated capacity , arises as the limit situation of a family of heat transmission problems between the original body and an outer neighbourhood of Γ where the heat conductivity goes increasing in a privileged direction. The phase‐field model is adopted for the physical description. The concentrated capacity formulation is directly addressed in its variational setting and an existence and uniqueness theorem is proved by means of approximation techniques for parabolic systems (Faedo–Galerkin scheme, Yosida regularization). Copyright © 1999 John Wiley & Sons, Ltd.