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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Abstract

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.

About the authors

M. N. Zubova

Lomonosov Moscow State University

Email: shaposh.tan@mail.ru
Russian Federation, 1, Leninskie gory, Moscow, 119991

T. A. Shaposhnikova

Lomonosov Moscow State University

Author for correspondence.
Email: shaposh.tan@mail.ru
Russian Federation, 1, Leninskie gory, Moscow, 119991

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