Asymptotic analysis of the spectral Neumann problem in thick multi-structure of type 3:1:1
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...
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| Veröffentlicht in: | Нелинейные граничные задачи |
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| Datum: | 2005 |
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| Format: | Artikel |
| Sprache: | Englisch |
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Інститут прикладної математики і механіки НАН України
2005
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/169156 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | 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. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862715101905158144 |
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| author | Mel'nyk, T.A. |
| author_facet | Mel'nyk, T.A. |
| citation_txt | 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. |
| collection | DSpace DC |
| container_title | Нелинейные граничные задачи |
| description | 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.
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| first_indexed | 2025-12-07T17:56:09Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-169156 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 0236-0497 |
| language | English |
| last_indexed | 2025-12-07T17:56:09Z |
| publishDate | 2005 |
| publisher | Інститут прикладної математики і механіки НАН України |
| record_format | dspace |
| spelling | Mel'nyk, T.A. 2020-06-06T18:07:41Z 2020-06-06T18:07:41Z 2005 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. 0236-0497 https://nasplib.isofts.kiev.ua/handle/123456789/169156 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. en Інститут прикладної математики і механіки НАН України Нелинейные граничные задачи Asymptotic analysis of the spectral Neumann problem in thick multi-structure of type 3:1:1 Article published earlier |
| spellingShingle | Asymptotic analysis of the spectral Neumann problem in thick multi-structure of type 3:1:1 Mel'nyk, T.A. |
| title | Asymptotic analysis of the spectral Neumann problem in thick multi-structure of type 3:1:1 |
| title_full | Asymptotic analysis of the spectral Neumann problem in thick multi-structure of type 3:1:1 |
| title_fullStr | Asymptotic analysis of the spectral Neumann problem in thick multi-structure of type 3:1:1 |
| title_full_unstemmed | Asymptotic analysis of the spectral Neumann problem in thick multi-structure of type 3:1:1 |
| title_short | Asymptotic analysis of the spectral Neumann problem in thick multi-structure of type 3:1:1 |
| title_sort | asymptotic analysis of the spectral neumann problem in thick multi-structure of type 3:1:1 |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/169156 |
| work_keys_str_mv | AT melnykta asymptoticanalysisofthespectralneumannprobleminthickmultistructureoftype311 |