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

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.