Homogenization of the Robin problem in a thick multilevel junction

We consider a mixed boundary-value problem for the Poisson equation in a plane two-level junction that is the union of a domain ₀ and a large number 2N of thin rods with variable thickness of order = (N ^–1). The thin rods are divided into two levels, depending on their length. In addition, the thin rods from each level are -periodically alternated. We investigate the asymptotic behavior of the solution as 0 under the Robin conditions on the boundaries of the thin rods. By using some special extension operators, a convergence theorem is proved.Published in Neliniini Kolyvannya, Vol. 7, No. 3, pp. 336–355, July–September, 2004.