Galerkin Method for First-Order Hyperbolic Systems with Two Independent Variables
We investigate a mixed problem for a weakly nonlinear first-order hyperbolic system with two independent variables in bounded and unbounded domains. Assuming that the nonlinearities are monotonic, we obtain conditions for the existence and uniqueness of a generalized solution; these conditions do no...
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| Date: | 2002 |
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| Main Authors: | , , , |
| Format: | Article |
| Language: | Ukrainian English |
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Institute of Mathematics, NAS of Ukraine
2002
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/4174 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860510308941955072 |
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| author | Lavrenyuk, S. P. Oliskevych, M. O. Лавренюк, С. П. Оліскевич, М. О. |
| author_facet | Lavrenyuk, S. P. Oliskevych, M. O. Лавренюк, С. П. Оліскевич, М. О. |
| author_sort | Lavrenyuk, S. P. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-18T20:23:51Z |
| description | We investigate a mixed problem for a weakly nonlinear first-order hyperbolic system with two independent variables in bounded and unbounded domains. Assuming that the nonlinearities are monotonic, we obtain conditions for the existence and uniqueness of a generalized solution; these conditions do not depend on the behavior of a solution as x → +∞. |
| first_indexed | 2026-03-24T02:54:56Z |
| format | Article |
| fulltext |
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| id | umjimathkievua-article-4174 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | Ukrainian English |
| last_indexed | 2026-03-24T02:54:56Z |
| publishDate | 2002 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/d5/12afb3d8f1535fc3e469a3657b75ffd5.pdf |
| spelling | umjimathkievua-article-41742020-03-18T20:23:51Z Galerkin Method for First-Order Hyperbolic Systems with Two Independent Variables Метод Гальоркіна для гіперболічних систем першого порядку з двома незалежними змінними Lavrenyuk, S. P. Oliskevych, M. O. Лавренюк, С. П. Оліскевич, М. О. We investigate a mixed problem for a weakly nonlinear first-order hyperbolic system with two independent variables in bounded and unbounded domains. Assuming that the nonlinearities are monotonic, we obtain conditions for the existence and uniqueness of a generalized solution; these conditions do not depend on the behavior of a solution as x → +∞. Досліджено мішану задачу для слабконелінійної гіперболічної системи першого порядку з двома незалежними змінними в обмеженій та необмеженій областях. За припущення монотонності нелінійностей отримано умови існування та єдипості узагальненого розв'язку незалежно від його поведінки при x → +∞. Institute of Mathematics, NAS of Ukraine 2002-10-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/4174 Ukrains’kyi Matematychnyi Zhurnal; Vol. 54 No. 10 (2002); 1356-1371 Український математичний журнал; Том 54 № 10 (2002); 1356-1371 1027-3190 uk en https://umj.imath.kiev.ua/index.php/umj/article/view/4174/5057 https://umj.imath.kiev.ua/index.php/umj/article/view/4174/5058 Copyright (c) 2002 Lavrenyuk S. P.; Oliskevych M. O. |
| spellingShingle | Lavrenyuk, S. P. Oliskevych, M. O. Лавренюк, С. П. Оліскевич, М. О. Galerkin Method for First-Order Hyperbolic Systems with Two Independent Variables |
| title | Galerkin Method for First-Order Hyperbolic Systems with Two Independent Variables |
| title_alt | Метод Гальоркіна для гіперболічних систем першого
порядку з двома незалежними змінними |
| title_full | Galerkin Method for First-Order Hyperbolic Systems with Two Independent Variables |
| title_fullStr | Galerkin Method for First-Order Hyperbolic Systems with Two Independent Variables |
| title_full_unstemmed | Galerkin Method for First-Order Hyperbolic Systems with Two Independent Variables |
| title_short | Galerkin Method for First-Order Hyperbolic Systems with Two Independent Variables |
| title_sort | galerkin method for first-order hyperbolic systems with two independent variables |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/4174 |
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