On a smooth solution of a nonlinear periodic boundary-value problem
We establish conditions for the existence of a smooth solution of a quasilinear hyperbolic equationu tt - uxx = ƒ(x, t, u, u, u x),u (0,t) = u (π,t) = 0,u (x, t+ T) = u (x, t), (x, t) ∈ [0, π] ×R, and prove a theorem on the existence and uniqueness of a solution.
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| Datum: | 1999 |
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| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Ukrainisch Englisch |
| Veröffentlicht: |
Institute of Mathematics, NAS of Ukraine
1999
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| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/4760 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860510926127497216 |
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| author | Dobrynskii, V. A. Домбровський, I. В. |
| author_facet | Dobrynskii, V. A. Домбровський, I. В. |
| author_sort | Dobrynskii, V. A. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-18T21:13:14Z |
| description | We establish conditions for the existence of a smooth solution of a quasilinear hyperbolic equationu tt - uxx = ƒ(x, t, u, u, u x),u (0,t) = u (π,t) = 0,u (x, t+ T) = u (x, t), (x, t) ∈ [0, π] ×R, and prove a theorem on the existence and uniqueness of a solution. |
| first_indexed | 2026-03-24T03:04:45Z |
| format | Article |
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| id | umjimathkievua-article-4760 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | Ukrainian English |
| last_indexed | 2026-03-24T03:04:45Z |
| publishDate | 1999 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/fe/26ef074164de074b519c56b42f28c7fe.pdf |
| spelling | umjimathkievua-article-47602020-03-18T21:13:14Z On a smooth solution of a nonlinear periodic boundary-value problem Гладкий розв'язок нелінійної крайової періодичної задачі Dobrynskii, V. A. Домбровський, I. В. We establish conditions for the existence of a smooth solution of a quasilinear hyperbolic equationu tt - uxx = ƒ(x, t, u, u, u x),u (0,t) = u (π,t) = 0,u (x, t+ T) = u (x, t), (x, t) ∈ [0, π] ×R, and prove a theorem on the existence and uniqueness of a solution. Знайдено умови існування гладкого розв'язку для квазілінійиого гіперболічного рівняння $u_{tt} - u_{xx} = ƒ(x, t, u, u, u_x),\; u(0,t) = u(π,t) = 0,\; u(x, t+ T) = u(x, t),\; (x, t) ∈ [0, π] × R, $. Доведено теорему існування єдиності розв'язку. Institute of Mathematics, NAS of Ukraine 1999-11-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/4760 Ukrains’kyi Matematychnyi Zhurnal; Vol. 51 No. 11 (1999); 1574–1576 Український математичний журнал; Том 51 № 11 (1999); 1574–1576 1027-3190 uk en https://umj.imath.kiev.ua/index.php/umj/article/view/4760/6221 https://umj.imath.kiev.ua/index.php/umj/article/view/4760/6222 Copyright (c) 1999 Dobrynskii V. A. |
| spellingShingle | Dobrynskii, V. A. Домбровський, I. В. On a smooth solution of a nonlinear periodic boundary-value problem |
| title | On a smooth solution of a nonlinear periodic boundary-value problem |
| title_alt | Гладкий розв'язок нелінійної крайової періодичної задачі |
| title_full | On a smooth solution of a nonlinear periodic boundary-value problem |
| title_fullStr | On a smooth solution of a nonlinear periodic boundary-value problem |
| title_full_unstemmed | On a smooth solution of a nonlinear periodic boundary-value problem |
| title_short | On a smooth solution of a nonlinear periodic boundary-value problem |
| title_sort | on a smooth solution of a nonlinear periodic boundary-value problem |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/4760 |
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