Homogenization of a Poisson boundary value problem in a plane thick two-level junction

In this paper we consider a mixed boundary-value problem for the Poisson equation in a plane two-level junction Ωε, which is the union of a domain Ω0 and a large number 2N of thin rods with variable thickness of order ε = O(Nì−1). The thin rods are divided into two levels depending on their lenght. In addition, the thin rods from each level are ε−periodically alternated. We investigate the asymptotic behaviour of the solution as ε → 0 under the Robin conditions on the boundaries of the thin rods. By using some special extension operators, the convergence theorem is proved.