Solutions of a time-asymmetric boundary-value problem for a third-order equation with variable coefficients
UDC 517.951 We study a boundary-value problem with asymmetric time conditions for a third-order inhomogeneous equation with multiple characteristics of lowest-order terms. The unique solvability of the problem is proved by the energy-integral method. It is shown that if the uniqueness condition i...
Gespeichert in:
| Datum: | 2026 |
|---|---|
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Englisch |
| Veröffentlicht: |
Institute of Mathematics, NAS of Ukraine
2026
|
| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/8975 |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
| Завантажити файл: | |
Institution
Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860513348884365312 |
|---|---|
| author | Apakov, Yusupjon Umarov, Raxmatilla Apakov, Yusupjon Umarov, Raxmatilla |
| author_facet | Apakov, Yusupjon Umarov, Raxmatilla Apakov, Yusupjon Umarov, Raxmatilla |
| author_sort | Apakov, Yusupjon |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2026-03-21T11:04:14Z |
| description | UDC 517.951
We study a boundary-value problem with asymmetric time conditions for a third-order inhomogeneous equation with multiple characteristics of lowest-order terms. The unique solvability of the problem is proved by the energy-integral method. It is shown that if the uniqueness condition is violated, then the homogeneous problem has a nontrivial solution. The existence is proved by the Fourier method. The solution of the stated problem is obtained in the explicit form by using the constructed Green's function. The uniform convergence of the solutions and their derivatives contained in the equation is proved. |
| doi_str_mv | 10.3842/umzh.v78i1-2.8975 |
| first_indexed | 2026-03-24T03:43:16Z |
| format | Article |
| fulltext | |
| id | umjimathkievua-article-8975 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | English |
| last_indexed | 2026-03-24T03:43:16Z |
| publishDate | 2026 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | |
| spelling | umjimathkievua-article-89752026-03-21T11:04:14Z Solutions of a time-asymmetric boundary-value problem for a third-order equation with variable coefficients Solutions of a time-asymmetric boundary-value problem for a third-order equation with variable coefficients Apakov, Yusupjon Umarov, Raxmatilla Apakov, Yusupjon Umarov, Raxmatilla Differential equation, third order, multiple characteristics, asymmetric boundary value problem, regular solution, uniqueness, existence, Green’s function. Диференціальне рівняння, третій порядок, множинні характеристики, несиметрична крайова задача, регулярний розв’язок, єдиність, існування, функція Гріна. UDC 517.951 We study a boundary-value problem with asymmetric time conditions for a third-order inhomogeneous equation with multiple characteristics of lowest-order terms. The unique solvability of the problem is proved by the energy-integral method. It is shown that if the uniqueness condition is violated, then the homogeneous problem has a nontrivial solution. The existence is proved by the Fourier method. The solution of the stated problem is obtained in the explicit form by using the constructed Green's function. The uniform convergence of the solutions and their derivatives contained in the equation is proved. УДК 517.951 Розв'язки часово-асиметричної крайової задачі для рівняння третього порядку зі змінними коефіцієнтами Досліджено крайову задачу з асиметричними часовими умовами для неоднорідного рівняння третього порядку з кратними характеристиками та членами найнижчого порядку. Єдиність розв'язку задачі доведено за допомогою методу енергетичного інтеграла. Показано, що у випадку порушення умови теореми про єдиність однорідна задача має нетривіальний розв'язок. Його існування встановленометодом Фур'є. Розв'язок поставленої задачі отримано в явному вигляді за допомогою побудованої функції Гріна. Доведено рівномірну збіжність розв'язку та його похідних, що входять у рівняння. Institute of Mathematics, NAS of Ukraine 2026-03-02 Article Article https://umj.imath.kiev.ua/index.php/umj/article/view/8975 10.3842/umzh.v78i1-2.8975 Ukrains’kyi Matematychnyi Zhurnal; Vol. 78 No. 1-2 (2026); 77–78 Український математичний журнал; Том 78 № 1-2 (2026); 77–78 1027-3190 en https://umj.imath.kiev.ua/index.php/umj/article/view/8975/10619 Copyright (c) 2026 Yusupjon Apakov, Raxmatilla Umarov |
| spellingShingle | Apakov, Yusupjon Umarov, Raxmatilla Apakov, Yusupjon Umarov, Raxmatilla Solutions of a time-asymmetric boundary-value problem for a third-order equation with variable coefficients |
| title | Solutions of a time-asymmetric boundary-value problem for a third-order equation with variable coefficients |
| title_alt | Solutions of a time-asymmetric boundary-value problem for a third-order equation with variable coefficients |
| title_full | Solutions of a time-asymmetric boundary-value problem for a third-order equation with variable coefficients |
| title_fullStr | Solutions of a time-asymmetric boundary-value problem for a third-order equation with variable coefficients |
| title_full_unstemmed | Solutions of a time-asymmetric boundary-value problem for a third-order equation with variable coefficients |
| title_short | Solutions of a time-asymmetric boundary-value problem for a third-order equation with variable coefficients |
| title_sort | solutions of a time-asymmetric boundary-value problem for a third-order equation with variable coefficients |
| topic_facet | Differential equation third order multiple characteristics asymmetric boundary value problem regular solution uniqueness existence Green’s function. Диференціальне рівняння третій порядок множинні характеристики несиметрична крайова задача регулярний розв’язок єдиність існування функція Гріна. |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/8975 |
| work_keys_str_mv | AT apakovyusupjon solutionsofatimeasymmetricboundaryvalueproblemforathirdorderequationwithvariablecoefficients AT umarovraxmatilla solutionsofatimeasymmetricboundaryvalueproblemforathirdorderequationwithvariablecoefficients AT apakovyusupjon solutionsofatimeasymmetricboundaryvalueproblemforathirdorderequationwithvariablecoefficients AT umarovraxmatilla solutionsofatimeasymmetricboundaryvalueproblemforathirdorderequationwithvariablecoefficients |