Homogenization of elliptic problems with alternating boundary conditions in a thick two-level junction of type 3:2:2

Abstract

The asymptotic behavior of solutions to boundary value problems for the Poisson equation is studied in a thick two-level junction of type 3:2:2 with alternating boundary conditions. The thick junction consists of a cylinder with e-periodically stringed thin disks of variable thickness. The disks are divided into two classes depending on their geometric structure and boundary conditions. We consider problems with alternating Dirichlet and Neumann boundary conditions and also problems with different alternating Fourier (Neumann) conditions. We study the influence of the boundary conditions on the asymptotic behavior of solutions as e → 0. Convergence theorems, in particular, convergence of energy integrals, are proved. Bibliography: 31 titles. Illustrations: 1 figure.