Appearance of a Nonlocal Monotone Operator in Transmission Conditions when Homogenizing the Poisson Equation in a Domain Perforated Along an (n − 1)-Dimensional Manifold by Sets of Arbitrary Shape and Critical Size with Nonlinear Dynamic Boundary Conditions on the Boundary of Perforations

Abstract

We construct and justify an efficient model arising when homogenizing the Poisson equation in an e-periodically perforated domain along an (n − 1)-dimensional manifold by sets of an arbitrary shape and critical size on the boundary of which we impose a nonlinear dynamic condition containing an absorption coefficient of the form e−k, where k takes the critical value (n − 1)/(n − 2), n ≥ 3. We show that the transmission conditions on the manifold contain a nonlocal monotone operator.