Asymptotic Analysis of a Parabolic Problem in a Thick Two-Level Junction
We consider an initial boundary value problem for the heat equation in a plane two-level junction Ωε; which is the union of a domain and a large number 2N of thin rods with the variable thickness of order ε = O(N^-1). The thin rods are divided into two levels depending on boundary conditions given o...
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| Date: | 2007 |
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| Main Authors: | , |
| Format: | Article |
| Language: | English |
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Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
2007
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/7611 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Asymptotic analysis of a parabolic problem in a thick two-level junction / T. Durante, T.A. Mel'nyk // Журн. мат. физики, анализа, геометрии. — 2007. — Т. 3, № 3. — С. 313-341. — Бібліогр.: 37 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862728677063655424 |
|---|---|
| author | Durante, T. Mel'nyk, T.A. |
| author_facet | Durante, T. Mel'nyk, T.A. |
| citation_txt | Asymptotic analysis of a parabolic problem in a thick two-level junction / T. Durante, T.A. Mel'nyk // Журн. мат. физики, анализа, геометрии. — 2007. — Т. 3, № 3. — С. 313-341. — Бібліогр.: 37 назв. — англ. |
| collection | DSpace DC |
| description | We consider an initial boundary value problem for the heat equation in a plane two-level junction Ωε; which is the union of a domain and a large number 2N of thin rods with the variable thickness of order ε = O(N^-1). The thin rods are divided into two levels depending on boundary conditions given on their sides. In addition, the boundary conditions depend on the parameters α ≥ 1 and β ≥ 1, and the thin rods from each level are ε-periodically alternated. The asymptotic analysis of this problem for different values of α and β is made as ε → 0. The leading terms of the asymptotic expansion for the solution are constructed, the asymptotic estimate in the Sobolev space L² (0; T; H¹(Ωε)) is obtained and the convergence theorem is proved with minimal conditions for the right-hand sides.
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| first_indexed | 2025-12-07T19:10:23Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-7611 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1812-9471 |
| language | English |
| last_indexed | 2025-12-07T19:10:23Z |
| publishDate | 2007 |
| publisher | Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
| record_format | dspace |
| spelling | Durante, T. Mel'nyk, T.A. 2010-04-06T09:07:19Z 2010-04-06T09:07:19Z 2007 Asymptotic analysis of a parabolic problem in a thick two-level junction / T. Durante, T.A. Mel'nyk // Журн. мат. физики, анализа, геометрии. — 2007. — Т. 3, № 3. — С. 313-341. — Бібліогр.: 37 назв. — англ. 1812-9471 https://nasplib.isofts.kiev.ua/handle/123456789/7611 We consider an initial boundary value problem for the heat equation in a plane two-level junction Ωε; which is the union of a domain and a large number 2N of thin rods with the variable thickness of order ε = O(N^-1). The thin rods are divided into two levels depending on boundary conditions given on their sides. In addition, the boundary conditions depend on the parameters α ≥ 1 and β ≥ 1, and the thin rods from each level are ε-periodically alternated. The asymptotic analysis of this problem for different values of α and β is made as ε → 0. The leading terms of the asymptotic expansion for the solution are constructed, the asymptotic estimate in the Sobolev space L² (0; T; H¹(Ωε)) is obtained and the convergence theorem is proved with minimal conditions for the right-hand sides. en Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України Asymptotic Analysis of a Parabolic Problem in a Thick Two-Level Junction Асимптотичний аналіз параболічної задачі в густому дворівневому з'єднанні Article published earlier |
| spellingShingle | Asymptotic Analysis of a Parabolic Problem in a Thick Two-Level Junction Durante, T. Mel'nyk, T.A. |
| title | Asymptotic Analysis of a Parabolic Problem in a Thick Two-Level Junction |
| title_alt | Асимптотичний аналіз параболічної задачі в густому дворівневому з'єднанні |
| title_full | Asymptotic Analysis of a Parabolic Problem in a Thick Two-Level Junction |
| title_fullStr | Asymptotic Analysis of a Parabolic Problem in a Thick Two-Level Junction |
| title_full_unstemmed | Asymptotic Analysis of a Parabolic Problem in a Thick Two-Level Junction |
| title_short | Asymptotic Analysis of a Parabolic Problem in a Thick Two-Level Junction |
| title_sort | asymptotic analysis of a parabolic problem in a thick two-level junction |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/7611 |
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