Boundary-value problems for Helmholtz equations in an angular domain. I
The boundary-value problems are investigated that arise when studying the diffraction of acoustic waves on an infinite cylinder with cross-section of an arbitrary shape situated inside a wedge so that the axis of the cylinder is parallel to the edge of the wedge. The potential theory is worked out w...
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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/5823 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860512044786122752 |
|---|---|
| author | Podlipenko, Yu. K. Подлипенко, Ю. К. Подлипенко, Ю. К. |
| author_facet | Podlipenko, Yu. K. Подлипенко, Ю. К. Подлипенко, Ю. К. |
| author_sort | Podlipenko, Yu. K. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-19T09:18:35Z |
| description | The boundary-value problems are investigated that arise when studying the diffraction of acoustic waves on an infinite cylinder with cross-section of an arbitrary shape situated inside a wedge so that the axis of the cylinder is parallel to the edge of the wedge. The potential theory is worked out which enables one to reduce these boundary-value problems to integral equations on a one-dimensional contour — the boundary of the cross-section of this cylinder. The theorems on existence and uniqueness of solutions to the boundary-value problems and the corresponding integral equations are proved. For this case, a principle of limit absorption is established. Effective algorithms for calculating the kernels of the integral operators are constructed. |
| first_indexed | 2026-03-24T03:22:32Z |
| format | Article |
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| id | umjimathkievua-article-5823 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | rus English |
| last_indexed | 2026-03-24T03:22:32Z |
| publishDate | 1993 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/86/6d6814fc68d8d474645cc39ab4998e86.pdf |
| spelling | umjimathkievua-article-58232020-03-19T09:18:35Z Boundary-value problems for Helmholtz equations in an angular domain. I Краевые задачи для уравнения Гельмгольца в угловой области. I Podlipenko, Yu. K. Подлипенко, Ю. К. Подлипенко, Ю. К. The boundary-value problems are investigated that arise when studying the diffraction of acoustic waves on an infinite cylinder with cross-section of an arbitrary shape situated inside a wedge so that the axis of the cylinder is parallel to the edge of the wedge. The potential theory is worked out which enables one to reduce these boundary-value problems to integral equations on a one-dimensional contour — the boundary of the cross-section of this cylinder. The theorems on existence and uniqueness of solutions to the boundary-value problems and the corresponding integral equations are proved. For this case, a principle of limit absorption is established. Effective algorithms for calculating the kernels of the integral operators are constructed. Вивчаються крайові задачі, що виникають при дослідженні дифракції акустичних хвиль на нескінченному циліндрі із довільною формою поперечного перерізу, який розташований в середині клина так, що вісь циліндра паралельна до ребра клина. Розвинуто теорію потенціала, що дозволяє звести вказані крайові задачі до інтегральних рівнянь на одновимірному контурі — межі перерізу циліндра. Доведено теореми існування та єдиності розв’язків крайових задач і відповідних їм інтегральних рівнянь. Встановлено принцип граничного поглинання для даної ситуації. Для обчислення ядер інтегральних операторів побудовано ефективні алгоритми. Institute of Mathematics, NAS of Ukraine 1993-03-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/5823 Ukrains’kyi Matematychnyi Zhurnal; Vol. 45 No. 3 (1993); 403–418 Український математичний журнал; Том 45 № 3 (1993); 403–418 1027-3190 rus en https://umj.imath.kiev.ua/index.php/umj/article/view/5823/8329 https://umj.imath.kiev.ua/index.php/umj/article/view/5823/8330 Copyright (c) 1993 Podlipenko Yu. K. |
| spellingShingle | Podlipenko, Yu. K. Подлипенко, Ю. К. Подлипенко, Ю. К. Boundary-value problems for Helmholtz equations in an angular domain. I |
| title | Boundary-value problems for Helmholtz equations in an angular domain. I |
| title_alt | Краевые задачи для уравнения Гельмгольца в угловой области. I |
| title_full | Boundary-value problems for Helmholtz equations in an angular domain. I |
| title_fullStr | Boundary-value problems for Helmholtz equations in an angular domain. I |
| title_full_unstemmed | Boundary-value problems for Helmholtz equations in an angular domain. I |
| title_short | Boundary-value problems for Helmholtz equations in an angular domain. I |
| title_sort | boundary-value problems for helmholtz equations in an angular domain. i |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/5823 |
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