ASYMPTOTIC APPROXIMATION FOR THE SOLUTION TO THE ROBIN PROBLEM IN A THICK MULTI-LEVEL JUNCTION

Abstract

We consider a mixed boundary-value problem for the Poisson equation in a plane two-level junction Ω ε , which is the union of a domain Ω 0 and a large number 2N of thin rods with variable thickness of order [Formula: see text]. The thin rods are divided into two levels depending on their length. In addition, the thin rods from each level are ε-periodically alternated. The Robin conditions are given on the lateral boundaries of the thin rods. Using the method of matched asymptotic expansions, we construct the asymptotic approximation for the solution as ε → 0 and prove the corresponding estimates in the Sobolev space H 1 (Ω ε ).