Blow-up of solutions to a coupled quasilinear viscoelastic wave system with nonlinear damping and source
We study the blow-up of the solution to a quasilinear viscoelastic wave system coupled by nonlinear sources. The system is of homogeneous Dirichlet boundary condition. The nonlinear damping and source are added to the equations. We assume that the relaxation functions are non-negative non-in...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Texas State University
2017-03-01
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| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2017/78/abstr.html |
| _version_ | 1819067056402726912 |
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| author | Xiaoying Zhang Shugen Chai Jieqiong Wu |
| author_facet | Xiaoying Zhang Shugen Chai Jieqiong Wu |
| author_sort | Xiaoying Zhang |
| collection | DOAJ |
| description | We study the blow-up of the solution to a quasilinear viscoelastic wave
system coupled by nonlinear sources. The system is of
homogeneous Dirichlet boundary condition. The nonlinear damping and source
are added to the equations. We assume that the relaxation functions
are non-negative non-increasing functions and the initial energy is
negative. The competition relations among the nonlinear principal parts
are not constant functions, the viscoelasticity terms, dampings and
sources are analyzed by using perturbed energy method.
The blow-up result is proved under some conditions on the nonlinear principal
parts, viscoelasticity terms, dampings and sources by a contradiction argument. |
| first_indexed | 2024-12-21T16:12:11Z |
| format | Article |
| id | doaj.art-b17de5c11fc1465a9b0ca9078671b7a4 |
| institution | Directory Open Access Journal |
| issn | 1072-6691 |
| language | English |
| last_indexed | 2024-12-21T16:12:11Z |
| publishDate | 2017-03-01 |
| publisher | Texas State University |
| record_format | Article |
| series | Electronic Journal of Differential Equations |
| spelling | doaj.art-b17de5c11fc1465a9b0ca9078671b7a42022-12-21T18:57:46ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912017-03-01201778,111Blow-up of solutions to a coupled quasilinear viscoelastic wave system with nonlinear damping and sourceXiaoying Zhang0Shugen Chai1Jieqiong Wu2 Shanxi Univ., Taiyuan, Shanxi, China Shanxi Univ., Taiyuan, Shanxi, China Shanxi Univ., Taiyuan, Shanxi, China We study the blow-up of the solution to a quasilinear viscoelastic wave system coupled by nonlinear sources. The system is of homogeneous Dirichlet boundary condition. The nonlinear damping and source are added to the equations. We assume that the relaxation functions are non-negative non-increasing functions and the initial energy is negative. The competition relations among the nonlinear principal parts are not constant functions, the viscoelasticity terms, dampings and sources are analyzed by using perturbed energy method. The blow-up result is proved under some conditions on the nonlinear principal parts, viscoelasticity terms, dampings and sources by a contradiction argument.http://ejde.math.txstate.edu/Volumes/2017/78/abstr.htmlBlow upquasilinear wave systemviscoelasticity |
| spellingShingle | Xiaoying Zhang Shugen Chai Jieqiong Wu Blow-up of solutions to a coupled quasilinear viscoelastic wave system with nonlinear damping and source Electronic Journal of Differential Equations Blow up quasilinear wave system viscoelasticity |
| title | Blow-up of solutions to a coupled quasilinear viscoelastic wave system with nonlinear damping and source |
| title_full | Blow-up of solutions to a coupled quasilinear viscoelastic wave system with nonlinear damping and source |
| title_fullStr | Blow-up of solutions to a coupled quasilinear viscoelastic wave system with nonlinear damping and source |
| title_full_unstemmed | Blow-up of solutions to a coupled quasilinear viscoelastic wave system with nonlinear damping and source |
| title_short | Blow-up of solutions to a coupled quasilinear viscoelastic wave system with nonlinear damping and source |
| title_sort | blow up of solutions to a coupled quasilinear viscoelastic wave system with nonlinear damping and source |
| topic | Blow up quasilinear wave system viscoelasticity |
| url | http://ejde.math.txstate.edu/Volumes/2017/78/abstr.html |
| work_keys_str_mv | AT xiaoyingzhang blowupofsolutionstoacoupledquasilinearviscoelasticwavesystemwithnonlineardampingandsource AT shugenchai blowupofsolutionstoacoupledquasilinearviscoelasticwavesystemwithnonlineardampingandsource AT jieqiongwu blowupofsolutionstoacoupledquasilinearviscoelasticwavesystemwithnonlineardampingandsource |