The solvability of a boundary-value periodic problem
In the space of functions B a 3+ ={g(x, t)=−g(−x, t)=g(x+2π, t)=−g(x, t+T3/2)=g(x, −t)}, we establish that if the condition aT 3 (2s−1)=4πk, (4πk, a (2s−1))=1, k ∈ ℤ, s ∈ ℕ, is satisfied, then the linear problem u u −a 2 u xx =g(x, t), u(0, t)=u(π, t)=0, u(x, t+T 3 )=u(x, t), ℝ2, is always...
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| Date: | 1997 |
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| Main Authors: | , , , |
| Format: | Article |
| Language: | Ukrainian English |
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Institute of Mathematics, NAS of Ukraine
1997
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/5006 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860511199624429568 |
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| author | Petrovskii, Ya. B. Khoma, G. P. Петрівський, Я. Б. Хома, Г. П. |
| author_facet | Petrovskii, Ya. B. Khoma, G. P. Петрівський, Я. Б. Хома, Г. П. |
| author_sort | Petrovskii, Ya. B. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-18T21:22:31Z |
| description | In the space of functions B a 3+ ={g(x, t)=−g(−x, t)=g(x+2π, t)=−g(x, t+T3/2)=g(x, −t)}, we establish that if the condition aT 3 (2s−1)=4πk, (4πk, a (2s−1))=1, k ∈ ℤ, s ∈ ℕ, is satisfied, then the linear problem u u −a 2 u xx =g(x, t), u(0, t)=u(π, t)=0, u(x, t+T 3 )=u(x, t), ℝ2, is always consistent. To prove this statement, we construct an exact solution in the form of an integral operator. |
| first_indexed | 2026-03-24T03:09:06Z |
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| id | umjimathkievua-article-5006 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | Ukrainian English |
| last_indexed | 2026-03-24T03:09:06Z |
| publishDate | 1997 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/84/50ff58c1218bdaa564723e4135609184.pdf |
| spelling | umjimathkievua-article-50062020-03-18T21:22:31Z The solvability of a boundary-value periodic problem Розв'язність однієї крайової періодичної задачі Petrovskii, Ya. B. Khoma, G. P. Петрівський, Я. Б. Хома, Г. П. In the space of functions B a 3+ ={g(x, t)=−g(−x, t)=g(x+2π, t)=−g(x, t+T3/2)=g(x, −t)}, we establish that if the condition aT 3 (2s−1)=4πk, (4πk, a (2s−1))=1, k ∈ ℤ, s ∈ ℕ, is satisfied, then the linear problem u u −a 2 u xx =g(x, t), u(0, t)=u(π, t)=0, u(x, t+T 3 )=u(x, t), ℝ2, is always consistent. To prove this statement, we construct an exact solution in the form of an integral operator. У просторі функцій B a 3+ ={g(x, t)=−g(−x, t)=g(x+2π, t)=−g(x, t+T3/2)=g(x, −t)} встановлено, що при виконанні умови aT 3 (2s−1)=4πk, (4πk, a (2s−1))=1, k ∈ ℤ, s ∈ ℕ, лінійна задача u u −a 2 u xx =g(x, t), u(0, t)=u(π, t)=0, u(x, t+T 3 )=u(x, t), ℝ2 завжди сумісна. Для доведення цього твердження побудовано точний розв'язок у вигляді інтегрального оператора. Institute of Mathematics, NAS of Ukraine 1997-02-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/5006 Ukrains’kyi Matematychnyi Zhurnal; Vol. 49 No. 2 (1997); 302–308 Український математичний журнал; Том 49 № 2 (1997); 302–308 1027-3190 uk en https://umj.imath.kiev.ua/index.php/umj/article/view/5006/6711 https://umj.imath.kiev.ua/index.php/umj/article/view/5006/6712 Copyright (c) 1997 Petrovskii Ya. B.; Khoma G. P. |
| spellingShingle | Petrovskii, Ya. B. Khoma, G. P. Петрівський, Я. Б. Хома, Г. П. The solvability of a boundary-value periodic problem |
| title | The solvability of a boundary-value periodic problem |
| title_alt | Розв'язність однієї крайової періодичної задачі |
| title_full | The solvability of a boundary-value periodic problem |
| title_fullStr | The solvability of a boundary-value periodic problem |
| title_full_unstemmed | The solvability of a boundary-value periodic problem |
| title_short | The solvability of a boundary-value periodic problem |
| title_sort | solvability of a boundary-value periodic problem |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/5006 |
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