Asymptotic analysis of a spectral problem in a periodic thick junction of type 3:2:1

Abstract

Convergence theorems and asymptotic estimates (as e → 0) are proved for eigenvalues and eigenfunctions of a mixed boundary value problem for the Lapiace operator in a junction Ω e of a domain Ω 0 and a large number N 2 of e-periodically situated thin cylinders with thickness of order e = O(N -1 ). We construct an extension operator that is only asymptotically bounded in e on the eigenfunctions in the Sobolev space H 1 . An approach based on the asymptotic theory of elliptic problem in singularly perturbed domains is used.