Blow-up of solutions for a nonlinear viscoelastic wave equation with initial data at arbitrary energy level
In this paper, we study a three-dimensional (3D) viscoelastic wave equation with nonlinear weak damping, supercritical sources and prescribed past history (Formula presented.), (Formula presented.): (Formula presented.) where the relaxation function k is monotone decreasing with (Formula presented.)...
| Main Authors: | , , |
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| Format: | Journal Article |
| Published: |
Taylor & Francis
2018
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| Online Access: | http://hdl.handle.net/20.500.11937/68131 |
| _version_ | 1848761751524343808 |
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| author | Sun, F. Liu, Lishan Wu, Yong Hong |
| author_facet | Sun, F. Liu, Lishan Wu, Yong Hong |
| author_sort | Sun, F. |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | In this paper, we study a three-dimensional (3D) viscoelastic wave equation with nonlinear weak damping, supercritical sources and prescribed past history (Formula presented.), (Formula presented.): (Formula presented.) where the relaxation function k is monotone decreasing with (Formula presented.), (Formula presented.) and (Formula presented.). When the source is stronger than dissipations, i.e. (Formula presented.), we obtain some finite time blow-up results with positive initial energy. In particular, we obtain the existence of certain solutions which blow up in finite time for initial data at arbitrary energy level. |
| first_indexed | 2025-11-14T10:36:39Z |
| format | Journal Article |
| id | curtin-20.500.11937-68131 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T10:36:39Z |
| publishDate | 2018 |
| publisher | Taylor & Francis |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-681312019-08-16T03:35:01Z Blow-up of solutions for a nonlinear viscoelastic wave equation with initial data at arbitrary energy level Sun, F. Liu, Lishan Wu, Yong Hong In this paper, we study a three-dimensional (3D) viscoelastic wave equation with nonlinear weak damping, supercritical sources and prescribed past history (Formula presented.), (Formula presented.): (Formula presented.) where the relaxation function k is monotone decreasing with (Formula presented.), (Formula presented.) and (Formula presented.). When the source is stronger than dissipations, i.e. (Formula presented.), we obtain some finite time blow-up results with positive initial energy. In particular, we obtain the existence of certain solutions which blow up in finite time for initial data at arbitrary energy level. 2018 Journal Article http://hdl.handle.net/20.500.11937/68131 10.1080/00036811.2018.1460812 Taylor & Francis restricted |
| spellingShingle | Sun, F. Liu, Lishan Wu, Yong Hong Blow-up of solutions for a nonlinear viscoelastic wave equation with initial data at arbitrary energy level |
| title | Blow-up of solutions for a nonlinear viscoelastic wave equation with initial data at arbitrary energy level |
| title_full | Blow-up of solutions for a nonlinear viscoelastic wave equation with initial data at arbitrary energy level |
| title_fullStr | Blow-up of solutions for a nonlinear viscoelastic wave equation with initial data at arbitrary energy level |
| title_full_unstemmed | Blow-up of solutions for a nonlinear viscoelastic wave equation with initial data at arbitrary energy level |
| title_short | Blow-up of solutions for a nonlinear viscoelastic wave equation with initial data at arbitrary energy level |
| title_sort | blow-up of solutions for a nonlinear viscoelastic wave equation with initial data at arbitrary energy level |
| url | http://hdl.handle.net/20.500.11937/68131 |