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...
Збережено в:
| Дата: | 2007 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
2007
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| 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. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| Резюме: | 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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