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 homogenizing 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 homogenized 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.