On a smooth solution of a boundary-value problem
We study a periodic boundary-value problem for the quasilinear equation u tt −u xx =F[u, u t , u x ], u(x, 0)=u(x, π)=0, u(x + ω, t) = u(x, t), x ∈ ℝ t ∈ [0, π], and establish conditions that guarantee the validity of a theorem on unique solvability.
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| Date: | 1998 |
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| Main Authors: | , |
| Format: | Article |
| Language: | Ukrainian English |
| Published: |
Institute of Mathematics, NAS of Ukraine
1998
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/4849 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860511023818080256 |
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| author | Tsynalko, P. V. Цинайко, П. В. |
| author_facet | Tsynalko, P. V. Цинайко, П. В. |
| author_sort | Tsynalko, P. V. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-18T21:15:33Z |
| description | We study a periodic boundary-value problem for the quasilinear equation u tt −u xx =F[u, u t , u x ], u(x, 0)=u(x, π)=0, u(x + ω, t) = u(x, t), x ∈ ℝ t ∈ [0, π], and establish conditions that guarantee the validity of a theorem on unique solvability. |
| first_indexed | 2026-03-24T03:06:18Z |
| format | Article |
| fulltext |
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| id | umjimathkievua-article-4849 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | Ukrainian English |
| last_indexed | 2026-03-24T03:06:18Z |
| publishDate | 1998 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/01/59d1eb384d185aba38f2196adcc51f01.pdf |
| spelling | umjimathkievua-article-48492020-03-18T21:15:33Z On a smooth solution of a boundary-value problem Про один гладкий розв'язок крайової задачі Tsynalko, P. V. Цинайко, П. В. We study a periodic boundary-value problem for the quasilinear equation u tt −u xx =F[u, u t , u x ], u(x, 0)=u(x, π)=0, u(x + ω, t) = u(x, t), x ∈ ℝ t ∈ [0, π], and establish conditions that guarantee the validity of a theorem on unique solvability. Вивчається крайова періодична задача для кназілінійного рівняння $ u_{tt} −u_{xx} = F[u, u_t, u_x], u(x, 0) = u(x, π) = 0, u(x + ω, t) = u(x, t), \;x ∈ ℝ t ∈ [0, π] $. Знайдено умови, при яких справедлива теорема единості і розв'язку. Institute of Mathematics, NAS of Ukraine 1998-09-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/4849 Ukrains’kyi Matematychnyi Zhurnal; Vol. 50 No. 9 (1998); 1293–1296 Український математичний журнал; Том 50 № 9 (1998); 1293–1296 1027-3190 uk en https://umj.imath.kiev.ua/index.php/umj/article/view/4849/6397 https://umj.imath.kiev.ua/index.php/umj/article/view/4849/6398 Copyright (c) 1998 Tsynalko P. V. |
| spellingShingle | Tsynalko, P. V. Цинайко, П. В. On a smooth solution of a boundary-value problem |
| title | On a smooth solution of a boundary-value problem |
| title_alt | Про один гладкий розв'язок крайової задачі |
| title_full | On a smooth solution of a boundary-value problem |
| title_fullStr | On a smooth solution of a boundary-value problem |
| title_full_unstemmed | On a smooth solution of a boundary-value problem |
| title_short | On a smooth solution of a boundary-value problem |
| title_sort | on a smooth solution of a boundary-value problem |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/4849 |
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