Integral Conditions for Convergence of Solutions of Non-Linear Robin's Problem in Strongly Perforated Domain
We consider a boundary-value problem for the Poisson equation in a strongly perforated domain Ωε = Ω\Fε ⊂ Rⁿ (n ≥ 2) with non-linear Robin's condition on the boundary of the perforating set Fε. The domain Ωε depends on the small parameter ε > 0 such that the set Fε becomes more and more loos...
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| Datum: | 2017 |
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| Hauptverfasser: | , , |
| Format: | Artikel |
| Sprache: | English |
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Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
2017
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| Schriftenreihe: | Журнал математической физики, анализа, геометрии |
| Online Zugang: | http://dspace.nbuv.gov.ua/handle/123456789/140576 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Integral Conditions for Convergence of Solutions of Non-Linear Robin's Problem in Strongly Perforated Domain / E.Ya. Khruslov, L.O. Khilkova, M.V. Goncharenko // Журнал математической физики, анализа, геометрии. — 2017. — Т. 13, № 3. — С. 283-313. — Бібліогр.: 17 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| Zusammenfassung: | We consider a boundary-value problem for the Poisson equation in a strongly perforated domain Ωε = Ω\Fε ⊂ Rⁿ (n ≥ 2) with non-linear Robin's condition on the boundary of the perforating set Fε. The domain Ωε depends on the small parameter ε > 0 such that the set Fε becomes more and more loosened and distributes more densely in the domain Ω as ε→0. We study the asymptotic behavior of the solution uε(x) of the problem as ε→0. A homogenized equation for the main term u(x) of the asymptotics of uε(x) is constructed and the integral conditions for the convergence of uε(x) to u(x) are formulated. |
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