Premium
Asymptotic analysis of a spectral problem in a periodic thick junction of type 3:2:1
Author(s) -
Mel'nyk T. A.
Publication year - 2000
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/(sici)1099-1476(20000310)23:4<321::aid-mma116>3.0.co;2-1
Subject(s) - mathematics , spectral analysis , type (biology) , mathematical analysis , asymptotic analysis , ecology , physics , quantum mechanics , biology , spectroscopy
Convergence theorems and asymptotic estimates (as ϵ →0) are proved for eigenvalues and eigenfunctions of a mixed boundary value problem for the Laplace operator in a junction Ω ϵ of a domain Ω 0 and a large number N 2 of ϵ ‐periodically situated thin cylinders with thickness of order ϵ = O ( N −1 ). We construct an extension operator that is only asymptotically bounded in ϵ 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. Copyright © 2000 John Wiley & Sons, Ltd.