A sufficient condition for finite-time blow-up of the coupled viscoelastic wave equations with arbitrary positive initial energy
Abstract This paper aims to investigate the blow-up characteristics of solutions to a system of coupled viscoelastic wave equations, where the strong damping term, the dispersive term, linear weak damping term, and coupled source term are taken into account. By employing the concavity method, we est...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2025-07-01
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| Series: | Journal of Inequalities and Applications |
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| Online Access: | https://doi.org/10.1186/s13660-025-03334-2 |
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| author | Qian Li Yanyuan Xing |
| author_facet | Qian Li Yanyuan Xing |
| author_sort | Qian Li |
| collection | DOAJ |
| description | Abstract This paper aims to investigate the blow-up characteristics of solutions to a system of coupled viscoelastic wave equations, where the strong damping term, the dispersive term, linear weak damping term, and coupled source term are taken into account. By employing the concavity method, we establish certain sufficient conditions on the initial data that lead to finite-time blow-up of the solutions with arbitrarily high initial energy. This study extends and enhances previous findings in the academic literature. |
| format | Article |
| id | doaj-art-e8ab8d1361b04e6cae82b4923c19cc48 |
| institution | Kabale University |
| issn | 1029-242X |
| language | English |
| publishDate | 2025-07-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of Inequalities and Applications |
| spelling | doaj-art-e8ab8d1361b04e6cae82b4923c19cc482025-08-20T03:42:02ZengSpringerOpenJournal of Inequalities and Applications1029-242X2025-07-012025111210.1186/s13660-025-03334-2A sufficient condition for finite-time blow-up of the coupled viscoelastic wave equations with arbitrary positive initial energyQian Li0Yanyuan Xing1Department of Mathematics, Changzhi UniversityDepartment of Mathematics, Changzhi UniversityAbstract This paper aims to investigate the blow-up characteristics of solutions to a system of coupled viscoelastic wave equations, where the strong damping term, the dispersive term, linear weak damping term, and coupled source term are taken into account. By employing the concavity method, we establish certain sufficient conditions on the initial data that lead to finite-time blow-up of the solutions with arbitrarily high initial energy. This study extends and enhances previous findings in the academic literature.https://doi.org/10.1186/s13660-025-03334-2Coupled viscoelastic equationsRelaxation functionBlow-upArbitrary positive initial energy |
| spellingShingle | Qian Li Yanyuan Xing A sufficient condition for finite-time blow-up of the coupled viscoelastic wave equations with arbitrary positive initial energy Journal of Inequalities and Applications Coupled viscoelastic equations Relaxation function Blow-up Arbitrary positive initial energy |
| title | A sufficient condition for finite-time blow-up of the coupled viscoelastic wave equations with arbitrary positive initial energy |
| title_full | A sufficient condition for finite-time blow-up of the coupled viscoelastic wave equations with arbitrary positive initial energy |
| title_fullStr | A sufficient condition for finite-time blow-up of the coupled viscoelastic wave equations with arbitrary positive initial energy |
| title_full_unstemmed | A sufficient condition for finite-time blow-up of the coupled viscoelastic wave equations with arbitrary positive initial energy |
| title_short | A sufficient condition for finite-time blow-up of the coupled viscoelastic wave equations with arbitrary positive initial energy |
| title_sort | sufficient condition for finite time blow up of the coupled viscoelastic wave equations with arbitrary positive initial energy |
| topic | Coupled viscoelastic equations Relaxation function Blow-up Arbitrary positive initial energy |
| url | https://doi.org/10.1186/s13660-025-03334-2 |
| work_keys_str_mv | AT qianli asufficientconditionforfinitetimeblowupofthecoupledviscoelasticwaveequationswitharbitrarypositiveinitialenergy AT yanyuanxing asufficientconditionforfinitetimeblowupofthecoupledviscoelasticwaveequationswitharbitrarypositiveinitialenergy AT qianli sufficientconditionforfinitetimeblowupofthecoupledviscoelasticwaveequationswitharbitrarypositiveinitialenergy AT yanyuanxing sufficientconditionforfinitetimeblowupofthecoupledviscoelasticwaveequationswitharbitrarypositiveinitialenergy |