Homogenization limit for the Diffusion Equation in a domain Perforated along (n - 1)-Dimensional Manifold with Dynamic Conditions on the Boundary of the Perforations: Critical Case
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The problem of homogenization the diffusion equation in a domain perforated along an (n - 1)-dimensional manifold with dynamic boundary conditions on the boundary of the perforations is studied. A homogenization model is constructed that is a transmission problem for the diffusion equation with the transmission conditions containing a term with memory. A theorem on the convergence of solutions of the original problem to the solution of the homogenized one is proved.
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2013 ◽
Vol 18
(6)
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pp. 1581-1610
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