Blow-Up and Global Existence Analysis for the Viscoelastic Wave Equation with a Frictional and a Kelvin-Voigt Damping
We are concerned in this paper with the initial boundary value problem for a quasilinear viscoelastic wave equation which is subject to a nonlinear action, to a nonlinear frictional damping, and to a Kelvin-Voigt damping, simultaneously. By utilizing a carefully chosen Lyapunov functional, we establ...
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Wiley
2018-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2018/8931856 |
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| author | Fosheng Wang Chengqiang Wang |
| author_facet | Fosheng Wang Chengqiang Wang |
| author_sort | Fosheng Wang |
| collection | DOAJ |
| description | We are concerned in this paper with the initial boundary value problem for a quasilinear viscoelastic wave equation which is subject to a nonlinear action, to a nonlinear frictional damping, and to a Kelvin-Voigt damping, simultaneously. By utilizing a carefully chosen Lyapunov functional, we establish first by the celebrated convexity argument a finite time blow-up criterion for the initial boundary value problem in question; we prove second by an a priori estimate argument that some solutions to the problem exists globally if the nonlinearity is “weaker,” in a certain sense, than the frictional damping, and if the viscoelastic damping is sufficiently strong. |
| format | Article |
| id | doaj-art-bae00830b1104ef5b4d24d9615009ef0 |
| institution | OA Journals |
| issn | 1687-9120 1687-9139 |
| language | English |
| publishDate | 2018-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Mathematical Physics |
| spelling | doaj-art-bae00830b1104ef5b4d24d9615009ef02025-08-20T02:18:42ZengWileyAdvances in Mathematical Physics1687-91201687-91392018-01-01201810.1155/2018/89318568931856Blow-Up and Global Existence Analysis for the Viscoelastic Wave Equation with a Frictional and a Kelvin-Voigt DampingFosheng Wang0Chengqiang Wang1School of Mathematics and Physics, Mianyang Teachers’ College, Mianyang 621000, ChinaSchool of Mathematics, Chengdu Normal University, Chengdu 611130, ChinaWe are concerned in this paper with the initial boundary value problem for a quasilinear viscoelastic wave equation which is subject to a nonlinear action, to a nonlinear frictional damping, and to a Kelvin-Voigt damping, simultaneously. By utilizing a carefully chosen Lyapunov functional, we establish first by the celebrated convexity argument a finite time blow-up criterion for the initial boundary value problem in question; we prove second by an a priori estimate argument that some solutions to the problem exists globally if the nonlinearity is “weaker,” in a certain sense, than the frictional damping, and if the viscoelastic damping is sufficiently strong.http://dx.doi.org/10.1155/2018/8931856 |
| spellingShingle | Fosheng Wang Chengqiang Wang Blow-Up and Global Existence Analysis for the Viscoelastic Wave Equation with a Frictional and a Kelvin-Voigt Damping Advances in Mathematical Physics |
| title | Blow-Up and Global Existence Analysis for the Viscoelastic Wave Equation with a Frictional and a Kelvin-Voigt Damping |
| title_full | Blow-Up and Global Existence Analysis for the Viscoelastic Wave Equation with a Frictional and a Kelvin-Voigt Damping |
| title_fullStr | Blow-Up and Global Existence Analysis for the Viscoelastic Wave Equation with a Frictional and a Kelvin-Voigt Damping |
| title_full_unstemmed | Blow-Up and Global Existence Analysis for the Viscoelastic Wave Equation with a Frictional and a Kelvin-Voigt Damping |
| title_short | Blow-Up and Global Existence Analysis for the Viscoelastic Wave Equation with a Frictional and a Kelvin-Voigt Damping |
| title_sort | blow up and global existence analysis for the viscoelastic wave equation with a frictional and a kelvin voigt damping |
| url | http://dx.doi.org/10.1155/2018/8931856 |
| work_keys_str_mv | AT foshengwang blowupandglobalexistenceanalysisfortheviscoelasticwaveequationwithafrictionalandakelvinvoigtdamping AT chengqiangwang blowupandglobalexistenceanalysisfortheviscoelasticwaveequationwithafrictionalandakelvinvoigtdamping |