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Homogenization of one-phase Stefan-type problems in periodic and random media. (English) Zbl 1197.35290
Summary: We investigate the homogenization of Stefan-type problems with oscillating diffusion coefficients. Both cases of periodic and random (stationary ergodic) mediums are considered. The proof relies on the coincidence of viscosity solutions and weak solutions (which are the time derivatives of the solutions of an obstacle problem) for the Stefan problem. This coincidence result is of independent interest.

MSC:
35Q79 PDEs in connection with classical thermodynamics and heat transfer
35Q35 PDEs in connection with fluid mechanics
35R35 Free boundary problems for PDEs
80A22 Stefan problems, phase changes, etc.
80M40 Homogenization for problems in thermodynamics and heat transfer
80M30 Variational methods applied to problems in thermodynamics and heat transfer
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