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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Бібліографічні деталі
Дата:2007
Автори: Durante, T., Mel'nyk, T.A.
Формат: Стаття
Мова:English
Опубліковано: Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України 2007
Онлайн доступ:http://dspace.nbuv.gov.ua/handle/123456789/7611
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Назва журналу:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Цитувати: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
id irk-123456789-7611
record_format dspace
spelling irk-123456789-76112010-04-07T12:00:38Z Asymptotic Analysis of a Parabolic Problem in a Thick Two-Level Junction Durante, T. Mel'nyk, T.A. 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. 2007 Article 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 http://dspace.nbuv.gov.ua/handle/123456789/7611 en Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection DSpace DC
language English
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.
format Article
author Durante, T.
Mel'nyk, T.A.
spellingShingle Durante, T.
Mel'nyk, T.A.
Asymptotic Analysis of a Parabolic Problem in a Thick Two-Level Junction
author_facet Durante, T.
Mel'nyk, T.A.
author_sort Durante, T.
title 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_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_sort asymptotic analysis of a parabolic problem in a thick two-level junction
publisher Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
publishDate 2007
url http://dspace.nbuv.gov.ua/handle/123456789/7611
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.
work_keys_str_mv AT durantet asymptoticanalysisofaparabolicprobleminathicktwoleveljunction
AT melnykta asymptoticanalysisofaparabolicprobleminathicktwoleveljunction
first_indexed 2023-10-18T16:37:56Z
last_indexed 2023-10-18T16:37:56Z
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