Blow-up for logarithmic viscoelastic equations with delay and acoustic boundary conditions
In the present work, we establish a blow-up criterion for viscoelastic wave equations with nonlinear damping, logarithmic source, delay in the velocity, and acoustic boundary conditions. Due to the nonlinear damping term, we cannot apply the concavity method introduced by Levine. Thus, we use the en...
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| Format: | Article |
| Language: | English |
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De Gruyter
2023-04-01
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| Series: | Advances in Nonlinear Analysis |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/anona-2022-0310 |
| _version_ | 1827953075181060096 |
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| author | Park Sun-Hye |
| author_facet | Park Sun-Hye |
| author_sort | Park Sun-Hye |
| collection | DOAJ |
| description | In the present work, we establish a blow-up criterion for viscoelastic wave equations with nonlinear damping, logarithmic source, delay in the velocity, and acoustic boundary conditions. Due to the nonlinear damping term, we cannot apply the concavity method introduced by Levine. Thus, we use the energy method to show that the solution with negative initial energy blows up after finite time. Furthermore, we investigate the upper and lower bounds of the blow-up time. |
| first_indexed | 2024-04-09T14:08:26Z |
| format | Article |
| id | doaj.art-1fd2f2b4021d4901bac4a8701339b4b0 |
| institution | Directory Open Access Journal |
| issn | 2191-950X |
| language | English |
| last_indexed | 2024-04-09T14:08:26Z |
| publishDate | 2023-04-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Advances in Nonlinear Analysis |
| spelling | doaj.art-1fd2f2b4021d4901bac4a8701339b4b02023-05-06T15:50:46ZengDe GruyterAdvances in Nonlinear Analysis2191-950X2023-04-011215576558710.1515/anona-2022-0310Blow-up for logarithmic viscoelastic equations with delay and acoustic boundary conditionsPark Sun-Hye0Office for Education Accreditation, Pusan National University, Keumjeong-gu 46241, Busan, South KoreaIn the present work, we establish a blow-up criterion for viscoelastic wave equations with nonlinear damping, logarithmic source, delay in the velocity, and acoustic boundary conditions. Due to the nonlinear damping term, we cannot apply the concavity method introduced by Levine. Thus, we use the energy method to show that the solution with negative initial energy blows up after finite time. Furthermore, we investigate the upper and lower bounds of the blow-up time.https://doi.org/10.1515/anona-2022-0310blow-upviscoelastic equationlogarithmic nonlinearitytime delayacoustic boundary conditionnonlinear dissipation35l0535l7035b44 |
| spellingShingle | Park Sun-Hye Blow-up for logarithmic viscoelastic equations with delay and acoustic boundary conditions Advances in Nonlinear Analysis blow-up viscoelastic equation logarithmic nonlinearity time delay acoustic boundary condition nonlinear dissipation 35l05 35l70 35b44 |
| title | Blow-up for logarithmic viscoelastic equations with delay and acoustic boundary conditions |
| title_full | Blow-up for logarithmic viscoelastic equations with delay and acoustic boundary conditions |
| title_fullStr | Blow-up for logarithmic viscoelastic equations with delay and acoustic boundary conditions |
| title_full_unstemmed | Blow-up for logarithmic viscoelastic equations with delay and acoustic boundary conditions |
| title_short | Blow-up for logarithmic viscoelastic equations with delay and acoustic boundary conditions |
| title_sort | blow up for logarithmic viscoelastic equations with delay and acoustic boundary conditions |
| topic | blow-up viscoelastic equation logarithmic nonlinearity time delay acoustic boundary condition nonlinear dissipation 35l05 35l70 35b44 |
| url | https://doi.org/10.1515/anona-2022-0310 |
| work_keys_str_mv | AT parksunhye blowupforlogarithmicviscoelasticequationswithdelayandacousticboundaryconditions |