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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| Дата: | 2005 |
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| Автор: | |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут прикладної математики і механіки НАН України
2005
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| Назва видання: | Нелинейные граничные задачи |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/169156 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | 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. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
irk-123456789-169156 |
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irk-123456789-1691562020-06-07T01:26:24Z Asymptotic analysis of the spectral Neumann problem in thick multi-structure of type 3:1:1 Mel'nyk, T.A. 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. 2005 Article 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 http://dspace.nbuv.gov.ua/handle/123456789/169156 en Нелинейные граничные задачи Інститут прикладної математики і механіки НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| 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. |
| format |
Article |
| author |
Mel'nyk, T.A. |
| spellingShingle |
Mel'nyk, T.A. Asymptotic analysis of the spectral Neumann problem in thick multi-structure of type 3:1:1 Нелинейные граничные задачи |
| author_facet |
Mel'nyk, T.A. |
| author_sort |
Mel'nyk, T.A. |
| title |
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_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_sort |
asymptotic analysis of the spectral neumann problem in thick multi-structure of type 3:1:1 |
| publisher |
Інститут прикладної математики і механіки НАН України |
| publishDate |
2005 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/169156 |
| 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. |
| series |
Нелинейные граничные задачи |
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AT melnykta asymptoticanalysisofthespectralneumannprobleminthickmultistructureoftype311 |
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2023-10-18T22:24:33Z |
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2023-10-18T22:24:33Z |
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1796155439517270016 |