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Homogenization of a parabolic problem with an imperfect interface. (English) Zbl 1199.35015

The authors describe heat diffusion in a two-component composite conductor with an \(\varepsilon\)-periodic interface. Due to an imperfect contact on the interface, the heat flow through the interface is proportional to the jump of the temperature field by a factor of order \(\varepsilon^\gamma.\) They study the limit behaviour of this parabolic problem when the parameter \(\varepsilon\) tends to zero and describe the different homogenized (limit) problems, according to the value of \(\gamma.\) When \(\gamma = 1,\) a memory effect appears in the limit problem.

MSC:

35B27 Homogenization in context of PDEs; PDEs in media with periodic structure
35K51 Initial-boundary value problems for second-order parabolic systems
82B24 Interface problems; diffusion-limited aggregation arising in equilibrium statistical mechanics
80A99 Thermodynamics and heat transfer
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