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Asymptotic analysis of the spectral Neumann problem in thick multi-structure of type 3:1:1

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dc.contributor.author Mel'nyk, T.A.
dc.date.accessioned 2020-06-06T18:07:41Z
dc.date.available 2020-06-06T18:07:41Z
dc.date.issued 2005
dc.identifier.citation Asymptotic analysis of the spectral Neumann problem in thick multi-structure of type 3:1:1 / T.A. Mel'nyk // Нелинейные граничные задачи. — 2005. — Т. 15. — С. 85-98. — Бібліогр.: 12 назв. — англ. uk_UA
dc.identifier.issn 0236-0497
dc.identifier.uri http://dspace.nbuv.gov.ua/handle/123456789/169156
dc.description.abstract The spectral Neumann problem is considered in a thick multi-structure, which is the union of some three-dimensional domain (the junction’s body) and a large number of ε-periodically situated thin cylinders along some curve (the joint zone) on the boundary of junction’s body. The asymptotic behaviour (as ε → 0) of the eigenvalues and eigenfunctions is investigated. Three spectral problems form asymptotics for the eigenvalues and eigenfunctions of this problem, namely, the spectral Neumann problem in junction's body; some spectral problem in a plane domain, which is filled up by the thin cylinders in the limit passage (each eigenvalue of this problem has infinite multiplicity); and the spectral problem for some singular integral operator given on the joint zone. The Hausdorff convergence of the spectrum is proved, the leading terms of asymptotics are constructed (as ε → 0) and asymptotic estimates are justified for the eigenvalues and the eigenfunctions. uk_UA
dc.language.iso en uk_UA
dc.publisher Інститут прикладної математики і механіки НАН України uk_UA
dc.relation.ispartof Нелинейные граничные задачи
dc.title Asymptotic analysis of the spectral Neumann problem in thick multi-structure of type 3:1:1 uk_UA
dc.type Article uk_UA
dc.status published earlier uk_UA


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