Homogenization of the Robin problem in a thick multilevel junction
In the paper 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 2N of thin rods with variable thickness of order ε = O(N⁻¹). The thin rods are divided into two levels depending on their length....
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| Date: | 2004 |
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| Main Authors: | , , |
| Format: | Article |
| Language: | English |
| Published: |
Інститут математики НАН України
2004
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| Series: | Нелінійні коливання |
| Online Access: | http://dspace.nbuv.gov.ua/handle/123456789/177021 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Homogenization of the Robin problem in a thick multilevel junction / U.De Maio, T.A. Mel'nyk, C. Perugia // Нелінійні коливання. — 2004. — Т. 7, № 3. — С. 336-355. — Бібліогр.: 6 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| Summary: | In the paper 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 2N of thin rods with variable 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. We investigate the asymptotic behaviour of the
solution as ε → 0 under the Robin conditions on the boundaries of the thin rods. By using some special
extension operators, the convergence theorem is proved. |
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