Homogenization of Boundary Value Problems in Two-Level Thick Junctions Consisting of Thin Disks with Rounded or Sharp Edges

Abstract

We consider a linear elliptic boundary value problem in a two-level thick junction of type 3 : 2 : 2 which consists of a cylinder with e-periodically stringed thin disks. The thin disks are divided into two levels depending on their geometric structure and boundary conditions on their surfaces. The first-level thin disks have variable thickness vanishing at their edges. Hence some coefficients of the corresponding homogenized problem degenerate and its solution has a singular behavior near the boundary. We extract three qualitatively different cases of the asymptotic behavior of the solution as e → 0. Bibliography: 26 titles. Illustrations: 2 figures.