Asymptotic approximation for the solution to a boundary-value problem with varying type of boundary conditions in a thick two-level junction
We consider a mixed boundary-value problem for the Poisson equation in a plane two-level junction Ωε, which is the union of a domain Ω₀ and a large number 3N of thin rods with thickness of order ε = O(N⁻¹). The thin rods are divided into two levels depending on their length. In addition, the thin ro...
Збережено в:
| Дата: | 2006 |
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| Автори: | , , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2006
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| Назва видання: | Нелінійні коливання |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/178375 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Asymptotic approximation for the solution to a boundary-value problem with varying type of boundary conditions in a thick two-level junction / T. Durante, T.A. Mel'nyk, P.S. Vashchuk // Нелінійні коливання. — 2006. — Т. 9, № 3. — С. 336-355. — Бібліогр.: 22 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| Резюме: | We consider a mixed boundary-value problem for the Poisson equation in a plane two-level junction Ωε, which is the union of a domain Ω₀ and a large number 3N of thin rods with thickness of order ε = O(N⁻¹). The thin rods are divided into two levels depending on their length. In addition, the thin rods from each level are ε-periodically alternated. The uniform Dirichlet conditions and the nonuniform Neumann conditions are given respectively on the sides of the thin rods from the first level and the second level. Using the method of matched asymptotic expansions and special junction-layer solutions, we construct the asymptotic approximation for the solution and prove the corresponding estimates in the Sobolev space H¹ (Ωε) as ε → 0 (N → +∞). |
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