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Homogenization for heat transfer in polycrystals with interfacial resistances. (English) Zbl 1024.80005

Summary: Heat conduction is investigated in periodic (single- or multi-phase) microstructures having disconnected phases and resistances on the interfaces between the phases. After deriving uniform a priori estimates for the microsolutions the macroscopic equations are obtained rigorously by means of two-scale convergence. The required generalization of two scale convergence for surfaces is shown with the help of a Weyl decomposition in the context of Sobolev spaces with respect to measures.

MSC:

80M40 Homogenization for problems in thermodynamics and heat transfer
35B27 Homogenization in context of PDEs; PDEs in media with periodic structure
35J25 Boundary value problems for second-order elliptic equations
74Q05 Homogenization in equilibrium problems of solid mechanics
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