Homogenization of a Singularly Perturbed Parabolic Problem in a Thick Periodic Junction of the Type 3:2:1
We prove a convergence theorem and obtain asymptotic (as ε → 0) estimates for a solution of a parabolic initial boundary-value problem in a junction Ωε that consists of a domain Ω0 and a large number N 2 of ε-periodically located thin cylinders whose thickness is of order ε = O(N −1).
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| Date: | 2000 |
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| Main Authors: | , |
| Format: | Article |
| Language: | Ukrainian English |
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Institute of Mathematics, NAS of Ukraine
2000
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/4558 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860510702133837824 |
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| author | Mel'nik, T. A. Мельник, Т. А. |
| author_facet | Mel'nik, T. A. Мельник, Т. А. |
| author_sort | Mel'nik, T. A. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-18T20:31:24Z |
| description | We prove a convergence theorem and obtain asymptotic (as ε → 0) estimates for a solution of a parabolic initial boundary-value problem in a junction Ωε that consists of a domain Ω0 and a large number N 2 of ε-periodically located thin cylinders whose thickness is of order ε = O(N −1). |
| first_indexed | 2026-03-24T03:01:12Z |
| format | Article |
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| id | umjimathkievua-article-4558 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | Ukrainian English |
| last_indexed | 2026-03-24T03:01:12Z |
| publishDate | 2000 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/cc/75bf3d672b25c50de99dfb616e75cfcc.pdf |
| spelling | umjimathkievua-article-45582020-03-18T20:31:24Z Homogenization of a Singularly Perturbed Parabolic Problem in a Thick Periodic Junction of the Type 3:2:1 Усереднення сингулярно збуреної параболічної задачі в густому періодичному з'єднанні типу 3:2:1 Mel'nik, T. A. Мельник, Т. А. We prove a convergence theorem and obtain asymptotic (as ε → 0) estimates for a solution of a parabolic initial boundary-value problem in a junction Ωε that consists of a domain Ω0 and a large number N 2 of ε-periodically located thin cylinders whose thickness is of order ε = O(N −1). Доведено теорему збіжності та одержано асимптотичні оцінки (коли $ε → 0$) для розв'язку початково-крайової задачі параболічного типу в з'єднанні $Ω_ε$, яке складається з області $Ω_0$ та великої кількості $N^2$, $ε$-періодично розміщених тонких циліндрів товщиною порядку $ε = O(N^{−1})$. Institute of Mathematics, NAS of Ukraine 2000-11-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/4558 Ukrains’kyi Matematychnyi Zhurnal; Vol. 52 No. 11 (2000); 1524-1533 Український математичний журнал; Том 52 № 11 (2000); 1524-1533 1027-3190 uk en https://umj.imath.kiev.ua/index.php/umj/article/view/4558/5820 https://umj.imath.kiev.ua/index.php/umj/article/view/4558/5821 Copyright (c) 2000 Mel'nik T. A. |
| spellingShingle | Mel'nik, T. A. Мельник, Т. А. Homogenization of a Singularly Perturbed Parabolic Problem in a Thick Periodic Junction of the Type 3:2:1 |
| title | Homogenization of a Singularly Perturbed Parabolic Problem in a Thick Periodic Junction of the Type 3:2:1 |
| title_alt | Усереднення сингулярно збуреної параболічної задачі в густому періодичному з'єднанні типу 3:2:1 |
| title_full | Homogenization of a Singularly Perturbed Parabolic Problem in a Thick Periodic Junction of the Type 3:2:1 |
| title_fullStr | Homogenization of a Singularly Perturbed Parabolic Problem in a Thick Periodic Junction of the Type 3:2:1 |
| title_full_unstemmed | Homogenization of a Singularly Perturbed Parabolic Problem in a Thick Periodic Junction of the Type 3:2:1 |
| title_short | Homogenization of a Singularly Perturbed Parabolic Problem in a Thick Periodic Junction of the Type 3:2:1 |
| title_sort | homogenization of a singularly perturbed parabolic problem in a thick periodic junction of the type 3:2:1 |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/4558 |
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