Homogenization of the Robin problem for the Poisson equation in a thick multi‐structure of type 3:2:2

Abstract

In this paper we study a mixed boundary value problem for the Poisson equation in a multi‐structure Ω_ε, which is the union of a domain Ω₀ and a large number N of ε‐periodically situated thin rings with variable thickness of order ε=𝒪(N⁻¹). By using some special extension operator, we prove a convergence theorem as ε→0 and investigate the asymptotic behaviour of the solution under the Robin conditions on the boundaries of the thin rings.