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The Stefan problem in heterogeneous media. (English) Zbl 0706.35139
The nonlinear heat-transfer equation in discontinuously heterogeneous, but piecewise homogeneous media is investigated. The existence of a weak solution in an enthalpy formulation is proved by using a Rothe method and a certain regularization of the contact conditions between the homogeneous subdomains. Phase transitions (described as a Stefan problem) and nonlinear boundary conditions are covered, too. Besides, the equation need not be of a strongly parabolic type.
Reviewer: T.Roubíček

35R35 Free boundary problems for PDEs
35K55 Nonlinear parabolic equations
35D05 Existence of generalized solutions of PDE (MSC2000)
80A20 Heat and mass transfer, heat flow (MSC2010)
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