Wave Breaking and Global Existence for the Generalized Periodic Camassa-Holm Equation with the Weak Dissipation
In this paper, a family of the weakly dissipative periodic Camassa-Holm type equation cubic and quartic nonlinearities is considered. The precise blow-up scenarios of strong solutions and several conditions on the initial data to guarantee blow-up of the induced solutions are described in detail. Fi...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Hindawi Limited
2022-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2022/6955014 |
| _version_ | 1797972503108255744 |
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| author | Ying Zhang Congming Peng |
| author_facet | Ying Zhang Congming Peng |
| author_sort | Ying Zhang |
| collection | DOAJ |
| description | In this paper, a family of the weakly dissipative periodic Camassa-Holm type equation cubic and quartic nonlinearities is considered. The precise blow-up scenarios of strong solutions and several conditions on the initial data to guarantee blow-up of the induced solutions are described in detail. Finally, we establish a sufficient condition for global solutions. |
| first_indexed | 2024-04-11T03:49:30Z |
| format | Article |
| id | doaj.art-2f1f6f4141a743c18a069a11117f8312 |
| institution | Directory Open Access Journal |
| issn | 1687-9139 |
| language | English |
| last_indexed | 2024-04-11T03:49:30Z |
| publishDate | 2022-01-01 |
| publisher | Hindawi Limited |
| record_format | Article |
| series | Advances in Mathematical Physics |
| spelling | doaj.art-2f1f6f4141a743c18a069a11117f83122023-01-02T02:12:55ZengHindawi LimitedAdvances in Mathematical Physics1687-91392022-01-01202210.1155/2022/6955014Wave Breaking and Global Existence for the Generalized Periodic Camassa-Holm Equation with the Weak DissipationYing Zhang0Congming Peng1School of Mathematics and StatisticsSchool of Mathematics and StatisticsIn this paper, a family of the weakly dissipative periodic Camassa-Holm type equation cubic and quartic nonlinearities is considered. The precise blow-up scenarios of strong solutions and several conditions on the initial data to guarantee blow-up of the induced solutions are described in detail. Finally, we establish a sufficient condition for global solutions.http://dx.doi.org/10.1155/2022/6955014 |
| spellingShingle | Ying Zhang Congming Peng Wave Breaking and Global Existence for the Generalized Periodic Camassa-Holm Equation with the Weak Dissipation Advances in Mathematical Physics |
| title | Wave Breaking and Global Existence for the Generalized Periodic Camassa-Holm Equation with the Weak Dissipation |
| title_full | Wave Breaking and Global Existence for the Generalized Periodic Camassa-Holm Equation with the Weak Dissipation |
| title_fullStr | Wave Breaking and Global Existence for the Generalized Periodic Camassa-Holm Equation with the Weak Dissipation |
| title_full_unstemmed | Wave Breaking and Global Existence for the Generalized Periodic Camassa-Holm Equation with the Weak Dissipation |
| title_short | Wave Breaking and Global Existence for the Generalized Periodic Camassa-Holm Equation with the Weak Dissipation |
| title_sort | wave breaking and global existence for the generalized periodic camassa holm equation with the weak dissipation |
| url | http://dx.doi.org/10.1155/2022/6955014 |
| work_keys_str_mv | AT yingzhang wavebreakingandglobalexistenceforthegeneralizedperiodiccamassaholmequationwiththeweakdissipation AT congmingpeng wavebreakingandglobalexistenceforthegeneralizedperiodiccamassaholmequationwiththeweakdissipation |