Variational formulations of nonlinear boundary-value problems with a free boundary in the theory of interaction of surface waves with acoustic fields
Variational problems equivalent to nonlinear evolutionary boundary-value problems with a free boundary are formulated. These problems arise in the theory of interaction of limited volumes of liquid, gas, and their interface with acoustic fields. It is proved that the principle of separation of motio...
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| Date: | 1993 |
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| Main Authors: | , , , |
| Format: | Article |
| Language: | Russian English |
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Institute of Mathematics, NAS of Ukraine
1993
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/5972 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860512195116269568 |
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| author | Lukovsky, I. O. Timokha, A. N. Луковский, И. А. Тимоха, А. Н. Луковский, И. А. Тимоха, А. Н. |
| author_facet | Lukovsky, I. O. Timokha, A. N. Луковский, И. А. Тимоха, А. Н. Луковский, И. А. Тимоха, А. Н. |
| author_sort | Lukovsky, I. O. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-19T09:22:20Z |
| description | Variational problems equivalent to nonlinear evolutionary boundary-value problems with a free boundary are formulated. These problems arise in the theory of interaction of limited volumes of liquid, gas, and their interface with acoustic fields. It is proved that the principle of separation of motions can be applied to these variational problems. The problem of a capillary-acoustic equilibrium form is given in a variational formulation. |
| first_indexed | 2026-03-24T03:24:55Z |
| format | Article |
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| id | umjimathkievua-article-5972 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | rus English |
| last_indexed | 2026-03-24T03:24:55Z |
| publishDate | 1993 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/87/605bd57ff5b0ed9094dca06c1af3da87.pdf |
| spelling | umjimathkievua-article-59722020-03-19T09:22:20Z Variational formulations of nonlinear boundary-value problems with a free boundary in the theory of interaction of surface waves with acoustic fields Вариационные формулировки нелинейных краевых задач со свободной границей теории взаимодействия поверхностных волн с акустическими полями Lukovsky, I. O. Timokha, A. N. Луковский, И. А. Тимоха, А. Н. Луковский, И. А. Тимоха, А. Н. Variational problems equivalent to nonlinear evolutionary boundary-value problems with a free boundary are formulated. These problems arise in the theory of interaction of limited volumes of liquid, gas, and their interface with acoustic fields. It is proved that the principle of separation of motions can be applied to these variational problems. The problem of a capillary-acoustic equilibrium form is given in a variational formulation. Сформульовані варіаційні задачі, еквівалентні нелінійним еволюційним крайовим задачам з вільною границею, які виникають у теорії взаємодії обмежених об’ємів рідини, газу та поверхні розділу з акустичними полями. Доведена можливість застосування в цих варіаційних задачах принципу розділення рухів та одержані варіаційні формулювання задачі про капілярно-звукову форму рівноваги. Institute of Mathematics, NAS of Ukraine 1993-12-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/5972 Ukrains’kyi Matematychnyi Zhurnal; Vol. 45 No. 12 (1993); 1642–1652 Український математичний журнал; Том 45 № 12 (1993); 1642–1652 1027-3190 rus en https://umj.imath.kiev.ua/index.php/umj/article/view/5972/8627 https://umj.imath.kiev.ua/index.php/umj/article/view/5972/8628 Copyright (c) 1993 Lukovsky I. O.; Timokha A. N. |
| spellingShingle | Lukovsky, I. O. Timokha, A. N. Луковский, И. А. Тимоха, А. Н. Луковский, И. А. Тимоха, А. Н. Variational formulations of nonlinear boundary-value problems with a free boundary in the theory of interaction of surface waves with acoustic fields |
| title | Variational formulations of nonlinear boundary-value problems with a free boundary in the theory of interaction of surface waves with acoustic fields |
| title_alt | Вариационные формулировки нелинейных краевых задач со свободной границей теории взаимодействия поверхностных волн с акустическими полями |
| title_full | Variational formulations of nonlinear boundary-value problems with a free boundary in the theory of interaction of surface waves with acoustic fields |
| title_fullStr | Variational formulations of nonlinear boundary-value problems with a free boundary in the theory of interaction of surface waves with acoustic fields |
| title_full_unstemmed | Variational formulations of nonlinear boundary-value problems with a free boundary in the theory of interaction of surface waves with acoustic fields |
| title_short | Variational formulations of nonlinear boundary-value problems with a free boundary in the theory of interaction of surface waves with acoustic fields |
| title_sort | variational formulations of nonlinear boundary-value problems with a free boundary in the theory of interaction of surface waves with acoustic fields |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/5972 |
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