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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| Published in: | Журнал математической физики, анализа, геометрии |
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| Date: | 2017 |
| Main Authors: | , , |
| Format: | Article |
| Language: | English |
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Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
2017
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/140576 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | 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| _version_ | 1862598230213132288 |
|---|---|
| author | Khruslov, E.Ya. Khilkova, L.O. Goncharenko, M.V. |
| author_facet | Khruslov, E.Ya. Khilkova, L.O. Goncharenko, M.V. |
| citation_txt | 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. |
| collection | DSpace DC |
| container_title | Журнал математической физики, анализа, геометрии |
| description | 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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| first_indexed | 2025-11-27T18:43:51Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-140576 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1812-9471 |
| language | English |
| last_indexed | 2025-11-27T18:43:51Z |
| publishDate | 2017 |
| publisher | Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
| record_format | dspace |
| spelling | Khruslov, E.Ya. Khilkova, L.O. Goncharenko, M.V. 2018-07-10T19:28:26Z 2018-07-10T19:28:26Z 2017 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. 1812-9471 Mathematics Subject Classification 2000: 35Q70 https://nasplib.isofts.kiev.ua/handle/123456789/140576 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. en Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України Журнал математической физики, анализа, геометрии Integral Conditions for Convergence of Solutions of Non-Linear Robin's Problem in Strongly Perforated Domain Article published earlier |
| spellingShingle | Integral Conditions for Convergence of Solutions of Non-Linear Robin's Problem in Strongly Perforated Domain Khruslov, E.Ya. Khilkova, L.O. Goncharenko, M.V. |
| title | Integral Conditions for Convergence of Solutions of Non-Linear Robin's Problem in Strongly Perforated Domain |
| title_full | Integral Conditions for Convergence of Solutions of Non-Linear Robin's Problem in Strongly Perforated Domain |
| title_fullStr | Integral Conditions for Convergence of Solutions of Non-Linear Robin's Problem in Strongly Perforated Domain |
| title_full_unstemmed | Integral Conditions for Convergence of Solutions of Non-Linear Robin's Problem in Strongly Perforated Domain |
| title_short | Integral Conditions for Convergence of Solutions of Non-Linear Robin's Problem in Strongly Perforated Domain |
| title_sort | integral conditions for convergence of solutions of non-linear robin's problem in strongly perforated domain |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/140576 |
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