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Weak solutions of a phase-field model for phase change of an alloy with thermal properties. (English) Zbl 1012.35049
The paper studies a model for phase change processes occurring in binary alloys with thermal effects which is expressed by a coupled system of nonlinear partial differential equations. A serious difficulty in treating the problem is the possibility of degeneracy of the parabolic character of the model. The existence of weak solutions is proved by using a regularization technique, compactness arguments and the Leray-Schauder theory.

MSC:
35K65 Degenerate parabolic equations
35R35 Free boundary problems for PDEs
80A22 Stefan problems, phase changes, etc.
35K55 Nonlinear parabolic equations
82B26 Phase transitions (general) in equilibrium statistical mechanics
82C26 Dynamic and nonequilibrium phase transitions (general) in statistical mechanics
35K50 Systems of parabolic equations, boundary value problems (MSC2000)
35B25 Singular perturbations in context of PDEs
35D05 Existence of generalized solutions of PDE (MSC2000)
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