Homogenization of a heat transfer problem in a highly heterogeneous periodic medium

摘要

We consider the homogenization of a heat transfer problem in a periodic media made of two connected components having comparable conductivities separated by a third medium (insulating layer), the thickness of which is of he same order ∈than the basic periodicity cell, and such that its conductance λ becomes infinitely small at the same time as ∈, following a rate λ=λ(∈). In the case where ∈~2/λ remains bounded, we identify the homogenized problem. Otherwise, we have to assume moreover that there are no sources in the third medium.