On boundary-value problems for a second-order differential equation with complex coefficients in a plane domain
We study boundary-value problems for a homogeneous partial differential equation of the second order with arbitrary constant complex coefficients and a homogeneous symbol in a bounded domain with smooth boundary. Necessary and sufficient conditions for the solvability of the Cauchy problem are obtai...
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| Date: | 1996 |
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| Main Authors: | , |
| Format: | Article |
| Language: | Russian English |
| Published: |
Institute of Mathematics, NAS of Ukraine
1996
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/5199 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860511406357479424 |
|---|---|
| author | Burskii, V. P. Бурский, В. П. Бурский, В. П. |
| author_facet | Burskii, V. P. Бурский, В. П. Бурский, В. П. |
| author_sort | Burskii, V. P. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-18T21:27:04Z |
| description | We study boundary-value problems for a homogeneous partial differential equation of the second order with arbitrary constant complex coefficients and a homogeneous symbol in a bounded domain with smooth boundary. Necessary and sufficient conditions for the solvability of the Cauchy problem are obtained. These conditions are written in the form of a moment problem on the boundary of the domain and applied to the investigation of boundary-value problems. This moment problem is solved in the case of a disk. |
| first_indexed | 2026-03-24T03:12:23Z |
| format | Article |
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| id | umjimathkievua-article-5199 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | rus English |
| last_indexed | 2026-03-24T03:12:23Z |
| publishDate | 1996 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/75/b18791b747b6634d14fd6b0c6905ff75.pdf |
| spelling | umjimathkievua-article-51992020-03-18T21:27:04Z On boundary-value problems for a second-order differential equation with complex coefficients in a plane domain О граничных задачах для дифференциального.уравнения с комплексными коэффициентами второго порядка в плоской области Burskii, V. P. Бурский, В. П. Бурский, В. П. We study boundary-value problems for a homogeneous partial differential equation of the second order with arbitrary constant complex coefficients and a homogeneous symbol in a bounded domain with smooth boundary. Necessary and sufficient conditions for the solvability of the Cauchy problem are obtained. These conditions are written in the form of a moment problem on the boundary of the domain and applied to the investigation of boundary-value problems. This moment problem is solved in the case of a disk. Вивчаються крайові задачі для однорідного диференціального рівняння з частинними похідними другого порядку з довільними постійними коефіцієнтами та одиорідиим символом в обмеженій області з гладкою межею. Одержані необхідні й достатні умови розв'язності задачі Коші, які зображаються у вигляді деякої проблеми моментів на межі області та застосовуються до вивчення граничних задач. Ця проблема моментів вивчається у випадку кола. Institute of Mathematics, NAS of Ukraine 1996-11-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/5199 Ukrains’kyi Matematychnyi Zhurnal; Vol. 48 No. 11 (1996); 1457-1467 Український математичний журнал; Том 48 № 11 (1996); 1457-1467 1027-3190 rus en https://umj.imath.kiev.ua/index.php/umj/article/view/5199/7092 https://umj.imath.kiev.ua/index.php/umj/article/view/5199/7093 Copyright (c) 1996 Burskii V. P. |
| spellingShingle | Burskii, V. P. Бурский, В. П. Бурский, В. П. On boundary-value problems for a second-order differential equation with complex coefficients in a plane domain |
| title | On boundary-value problems for a second-order differential equation with complex coefficients in a plane domain |
| title_alt | О граничных задачах для дифференциального.уравнения с
комплексными коэффициентами второго порядка в плоской области |
| title_full | On boundary-value problems for a second-order differential equation with complex coefficients in a plane domain |
| title_fullStr | On boundary-value problems for a second-order differential equation with complex coefficients in a plane domain |
| title_full_unstemmed | On boundary-value problems for a second-order differential equation with complex coefficients in a plane domain |
| title_short | On boundary-value problems for a second-order differential equation with complex coefficients in a plane domain |
| title_sort | on boundary-value problems for a second-order differential equation with complex coefficients in a plane domain |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/5199 |
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