A linear periodic boundary-value problem for a second-order hyperbolic equation
We study the boundary-value problemu tt -u xx =g(x, t),u(0,t) =u (π,t) = 0,u(x, t +T) =u(x, t), 0 ≤x ≤ π,t ∈ ℝ. We findexact classical solutions of this problem in three Vejvoda-Shtedry spaces, namely, in the classes of \(\frac{\pi }{q} - , \frac{{2\pi }}{{2s - 1}} - \) , and \(\frac{{4\pi }}...
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| Date: | 1999 |
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| Main Authors: | , , , |
| Format: | Article |
| Language: | Ukrainian English |
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Institute of Mathematics, NAS of Ukraine
1999
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/4611 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860510761260941312 |
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| author | Khoma, N. H. Khoma, L. G. Хома, H. Г. Хома, Л. Г. |
| author_facet | Khoma, N. H. Khoma, L. G. Хома, H. Г. Хома, Л. Г. |
| author_sort | Khoma, N. H. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-18T21:09:38Z |
| description | We study the boundary-value problemu tt -u xx =g(x, t),u(0,t) =u (π,t) = 0,u(x, t +T) =u(x, t), 0 ≤x ≤ π,t ∈ ℝ. We findexact classical solutions of this problem in three Vejvoda-Shtedry spaces, namely, in the classes of \(\frac{\pi }{q} - , \frac{{2\pi }}{{2s - 1}} - \) , and \(\frac{{4\pi }}{{2s - 1}}\) -periodic functions (q and s are natural numbers). We obtain the results only for sets of periods \(T_1 = (2p - 1)\frac{\pi }{q}, T_2 = (2p - 1)\frac{{2\pi }}{{2s - 1}}\) , and \(T_3 = (2p - 1)\frac{{4\pi }}{{2s - 1}}\) which characterize the classes of π-, 2π -, and 4π-periodic functions. |
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| id | umjimathkievua-article-4611 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | Ukrainian English |
| last_indexed | 2026-03-24T03:02:08Z |
| publishDate | 1999 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/d6/eab262fcd2b28a296c3131c7b7f50bd6.pdf |
| spelling | umjimathkievua-article-46112020-03-18T21:09:38Z A linear periodic boundary-value problem for a second-order hyperbolic equation Лінійна крайова періодична задача для гіперболічного рівняння другого порядку Khoma, N. H. Khoma, L. G. Хома, H. Г. Хома, Л. Г. We study the boundary-value problemu tt -u xx =g(x, t),u(0,t) =u (π,t) = 0,u(x, t +T) =u(x, t), 0 ≤x ≤ π,t ∈ ℝ. We findexact classical solutions of this problem in three Vejvoda-Shtedry spaces, namely, in the classes of \(\frac{\pi }{q} - , \frac{{2\pi }}{{2s - 1}} - \) , and \(\frac{{4\pi }}{{2s - 1}}\) -periodic functions (q and s are natural numbers). We obtain the results only for sets of periods \(T_1 = (2p - 1)\frac{\pi }{q}, T_2 = (2p - 1)\frac{{2\pi }}{{2s - 1}}\) , and \(T_3 = (2p - 1)\frac{{4\pi }}{{2s - 1}}\) which characterize the classes of π-, 2π -, and 4π-periodic functions. Вивчається крайова періодична задача $tt^{-u}_{xx } = g(x, t), \; u(0,t) = u (π,t) = 0,\; u(x, t + T) = u(x, t),\; 0 ≤x ≤ π,\; t ∈ ℝ$. В трьох просторах Вейводи - Штедри знайдено точні класичні розв язки даної задачі, а саме в класах $\frac{\pi }{q} - , \frac{{2\pi }}{{2s - 1}} -$, $\frac{{4\pi }}{{2s - 1}}$ -періодичних функцій ( $q, s$ — натуральні числа). Результати одержано лише для множин періодів $T_1 = (2p - 1)\frac{\pi }{q}, T_2 = (2p - 1)\frac{{2\pi }}{{2s - 1}}$, $T_3 = (2p - 1)\frac{{4\pi }}{{2s - 1}}$ що характеризують класи $π-, 2π -, 4π-$-періодичних функцій. Institute of Mathematics, NAS of Ukraine 1999-02-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/4611 Ukrains’kyi Matematychnyi Zhurnal; Vol. 51 No. 2 (1999); 281–284 Український математичний журнал; Том 51 № 2 (1999); 281–284 1027-3190 uk en https://umj.imath.kiev.ua/index.php/umj/article/view/4611/5925 https://umj.imath.kiev.ua/index.php/umj/article/view/4611/5926 Copyright (c) 1999 Khoma N. H.; Khoma L. G. |
| spellingShingle | Khoma, N. H. Khoma, L. G. Хома, H. Г. Хома, Л. Г. A linear periodic boundary-value problem for a second-order hyperbolic equation |
| title | A linear periodic boundary-value problem for a second-order hyperbolic equation |
| title_alt | Лінійна крайова періодична задача для гіперболічного рівняння
другого порядку |
| title_full | A linear periodic boundary-value problem for a second-order hyperbolic equation |
| title_fullStr | A linear periodic boundary-value problem for a second-order hyperbolic equation |
| title_full_unstemmed | A linear periodic boundary-value problem for a second-order hyperbolic equation |
| title_short | A linear periodic boundary-value problem for a second-order hyperbolic equation |
| title_sort | linear periodic boundary-value problem for a second-order hyperbolic equation |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/4611 |
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