Nonexistence of global solutions of abstract wave equations with high energies
Abstract We consider an undamped second order in time evolution equation. For any positive value of the initial energy, we give sufficient conditions to conclude nonexistence of global solutions. The analysis is based on a differential inequality. The success of our result is based in a detailed ana...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2017-10-01
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| Series: | Journal of Inequalities and Applications |
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| Online Access: | http://link.springer.com/article/10.1186/s13660-017-1546-1 |
| _version_ | 1817980341699215360 |
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| author | Jorge A Esquivel-Avila |
| author_facet | Jorge A Esquivel-Avila |
| author_sort | Jorge A Esquivel-Avila |
| collection | DOAJ |
| description | Abstract We consider an undamped second order in time evolution equation. For any positive value of the initial energy, we give sufficient conditions to conclude nonexistence of global solutions. The analysis is based on a differential inequality. The success of our result is based in a detailed analysis which is different from the ones commonly used to prove blow-up. Several examples are given improving known results in the literature. |
| first_indexed | 2024-04-13T22:52:52Z |
| format | Article |
| id | doaj.art-42cba5246ee7448d9231d634c22e767f |
| institution | Directory Open Access Journal |
| issn | 1029-242X |
| language | English |
| last_indexed | 2024-04-13T22:52:52Z |
| publishDate | 2017-10-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of Inequalities and Applications |
| spelling | doaj.art-42cba5246ee7448d9231d634c22e767f2022-12-22T02:26:07ZengSpringerOpenJournal of Inequalities and Applications1029-242X2017-10-012017111410.1186/s13660-017-1546-1Nonexistence of global solutions of abstract wave equations with high energiesJorge A Esquivel-Avila0Departamento de Ciencias Básicas, Análisis Matemático y sus Aplicaciones, UAM-AzcapotzalcoAbstract We consider an undamped second order in time evolution equation. For any positive value of the initial energy, we give sufficient conditions to conclude nonexistence of global solutions. The analysis is based on a differential inequality. The success of our result is based in a detailed analysis which is different from the ones commonly used to prove blow-up. Several examples are given improving known results in the literature.http://link.springer.com/article/10.1186/s13660-017-1546-1abstract wave equationnonexistenceblow upglobal solutionshigh energies |
| spellingShingle | Jorge A Esquivel-Avila Nonexistence of global solutions of abstract wave equations with high energies Journal of Inequalities and Applications abstract wave equation nonexistence blow up global solutions high energies |
| title | Nonexistence of global solutions of abstract wave equations with high energies |
| title_full | Nonexistence of global solutions of abstract wave equations with high energies |
| title_fullStr | Nonexistence of global solutions of abstract wave equations with high energies |
| title_full_unstemmed | Nonexistence of global solutions of abstract wave equations with high energies |
| title_short | Nonexistence of global solutions of abstract wave equations with high energies |
| title_sort | nonexistence of global solutions of abstract wave equations with high energies |
| topic | abstract wave equation nonexistence blow up global solutions high energies |
| url | http://link.springer.com/article/10.1186/s13660-017-1546-1 |
| work_keys_str_mv | AT jorgeaesquivelavila nonexistenceofglobalsolutionsofabstractwaveequationswithhighenergies |