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

✍ Scribed by T. A. Mel'nyk

Publisher: John Wiley and Sons
Year: 2000
Tongue: English
Weight: 204 KB
Volume: 23
Category: Article
ISSN: 0170-4214
DOI: 10.1002/(sici)1099-1476(20000310)23:4<321::aid-mma116>3.0.co;2-1

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✦ Synopsis

Convergence theorems and asymptotic estimates (as P0) are proved for eigenvalues and eigenfunctions of a mixed boundary value problem for the Laplace operator in a junction C of a domain and a large number N of -periodically situated thin cylinders with thickness of order "O(N). We construct an extension operator that is only asymptotically bounded in on the eigenfunctions in the Sobolev space H. An approach based on the asymptotic theory of elliptic problem in singularly perturbed domains is used.

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