Global existence and finite time blow-up of solutions for the semilinear pseudo-parabolic equation with a memory term
© 2017 Informa UK Limited, trading as Taylor & Francis Group In this paper, we investigate the initial boundary value problem for a pseudo-parabolic equation under the influence of a linear memory term and a nonlinear source term (Formula presented.) where (Formula presented.) is a bounded dom...
| Main Authors: | , , |
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| Format: | Journal Article |
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Taylor & Francis
2017
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| Online Access: | http://hdl.handle.net/20.500.11937/62323 |
| _version_ | 1848760829876371456 |
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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 | © 2017 Informa UK Limited, trading as Taylor & Francis Group In this paper, we investigate the initial boundary value problem for a pseudo-parabolic equation under the influence of a linear memory term and a nonlinear source term (Formula presented.) where (Formula presented.) is a bounded domain in (Formula presented.) ((Formula presented.)) with a Dirichlet boundary condition. Under suitable assumptions on the initial data (Formula presented.) and the relaxation function g, we obtain the global existence and finite time blow-up of solutions with initial data at low energy level (i.e. (Formula presented.)), by using the Galerkin method, the concavity method and an improved potential well method involving time t. We also derive the upper bounds for the blow-up time. Finally, we obtain the existence of solutions which blow up in finite time with initial data at arbitrary energy level. |
| first_indexed | 2025-11-14T10:22:00Z |
| format | Journal Article |
| id | curtin-20.500.11937-62323 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T10:22:00Z |
| publishDate | 2017 |
| publisher | Taylor & Francis |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-623232018-02-01T05:57:06Z Global existence and finite time blow-up of solutions for the semilinear pseudo-parabolic equation with a memory term Sun, F. Liu, Lishan Wu, Yong Hong © 2017 Informa UK Limited, trading as Taylor & Francis Group In this paper, we investigate the initial boundary value problem for a pseudo-parabolic equation under the influence of a linear memory term and a nonlinear source term (Formula presented.) where (Formula presented.) is a bounded domain in (Formula presented.) ((Formula presented.)) with a Dirichlet boundary condition. Under suitable assumptions on the initial data (Formula presented.) and the relaxation function g, we obtain the global existence and finite time blow-up of solutions with initial data at low energy level (i.e. (Formula presented.)), by using the Galerkin method, the concavity method and an improved potential well method involving time t. We also derive the upper bounds for the blow-up time. Finally, we obtain the existence of solutions which blow up in finite time with initial data at arbitrary energy level. 2017 Journal Article http://hdl.handle.net/20.500.11937/62323 10.1080/00036811.2017.1400536 Taylor & Francis restricted |
| spellingShingle | Sun, F. Liu, Lishan Wu, Yong Hong Global existence and finite time blow-up of solutions for the semilinear pseudo-parabolic equation with a memory term |
| title | Global existence and finite time blow-up of solutions for the semilinear pseudo-parabolic equation with a memory term |
| title_full | Global existence and finite time blow-up of solutions for the semilinear pseudo-parabolic equation with a memory term |
| title_fullStr | Global existence and finite time blow-up of solutions for the semilinear pseudo-parabolic equation with a memory term |
| title_full_unstemmed | Global existence and finite time blow-up of solutions for the semilinear pseudo-parabolic equation with a memory term |
| title_short | Global existence and finite time blow-up of solutions for the semilinear pseudo-parabolic equation with a memory term |
| title_sort | global existence and finite time blow-up of solutions for the semilinear pseudo-parabolic equation with a memory term |
| url | http://hdl.handle.net/20.500.11937/62323 |