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Dynamics of a free boundary in a binary medium with variable thermal conductivity. (English. Russian original) Zbl 0944.35114

Math. Notes 66, No. 2, 181-189 (1999); translation from Mat. Zametki 66, No. 2, 231-241 (1999).
Summary: We construct an asymptotic solution of the phase field system with variable thermal conductivity different in domains occupied by different phases. We show that, depending on relations between parameters characterizing the substance, the dynamics of the free interface between the phases is determined by solutions of the classical or modified Stefan problems.

MSC:

35R35 Free boundary problems for PDEs
80A22 Stefan problems, phase changes, etc.
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