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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| Дата: | 2017 |
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| Автори: | , , |
| Формат: | Стаття |
| Мова: | English |
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Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
2017
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| Назва видання: | Журнал математической физики, анализа, геометрии |
| Онлайн доступ: | 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 |
| Цитувати: | 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| id |
irk-123456789-140576 |
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irk-123456789-1405762018-07-11T01:23:36Z 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. 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. 2017 Article 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 http://dspace.nbuv.gov.ua/handle/123456789/140576 en Журнал математической физики, анализа, геометрии Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| 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. |
| format |
Article |
| author |
Khruslov, E.Ya. Khilkova, L.O. Goncharenko, M.V. |
| spellingShingle |
Khruslov, E.Ya. Khilkova, L.O. Goncharenko, M.V. Integral Conditions for Convergence of Solutions of Non-Linear Robin's Problem in Strongly Perforated Domain Журнал математической физики, анализа, геометрии |
| author_facet |
Khruslov, E.Ya. Khilkova, L.O. Goncharenko, M.V. |
| author_sort |
Khruslov, E.Ya. |
| title |
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_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_sort |
integral conditions for convergence of solutions of non-linear robin's problem in strongly perforated domain |
| publisher |
Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
| publishDate |
2017 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/140576 |
| 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. |
| series |
Журнал математической физики, анализа, геометрии |
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2023-10-18T21:22:58Z |
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2023-10-18T21:22:58Z |
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