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
Date:2017
Main Authors: Khruslov, E.Ya., Khilkova, L.O., Goncharenko, M.V.
Format: Article
Language:English
Published: Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України 2017
Online Access:https://nasplib.isofts.kiev.ua/handle/123456789/140576
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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
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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.
first_indexed 2025-11-27T18:43:51Z
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institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
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language English
last_indexed 2025-11-27T18:43:51Z
publishDate 2017
publisher Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
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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
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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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AT khilkovalo integralconditionsforconvergenceofsolutionsofnonlinearrobinsprobleminstronglyperforateddomain
AT goncharenkomv integralconditionsforconvergenceofsolutionsofnonlinearrobinsprobleminstronglyperforateddomain