Boundary Stabilization of a Nonlinear Viscoelastic Equation with Interior Time-Varying Delay and Nonlinear Dissipative Boundary Feedback
We investigate a nonlinear viscoelastic equation with interior time-varying delay and nonlinear dissipative boundary feedback. Under suitable assumptions on the relaxation function and time-varying delay effect together with nonlinear dissipative boundary feedback, we prove the global existence of...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/102594 |
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| _version_ | 1849398514188025856 |
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| author | Zaiyun Zhang Jianhua Huang Zhenhai Liu Mingbao Sun |
| author_facet | Zaiyun Zhang Jianhua Huang Zhenhai Liu Mingbao Sun |
| author_sort | Zaiyun Zhang |
| collection | DOAJ |
| description | We investigate a nonlinear viscoelastic equation with
interior time-varying delay and nonlinear dissipative boundary feedback.
Under suitable assumptions on the relaxation function and time-varying delay effect together with nonlinear dissipative boundary feedback, we
prove the global existence of weak solutions and asymptotic behavior of
the energy by using the Faedo-Galerkin method and the perturbed energy
method, respectively. This result improves earlier ones in the literature,
such as Kirane and Said-Houari (2011)
and Ammari et al. (2010). Moreover, we give an positive answer to the open
problem given by Kirane and Said-Houari (2011). |
| format | Article |
| id | doaj-art-a1bc92e41b3d43ddbb4c559b80de3134 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-a1bc92e41b3d43ddbb4c559b80de31342025-08-20T03:38:35ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/102594102594Boundary Stabilization of a Nonlinear Viscoelastic Equation with Interior Time-Varying Delay and Nonlinear Dissipative Boundary FeedbackZaiyun Zhang0Jianhua Huang1Zhenhai Liu2Mingbao Sun3College of Science, National University of Defense Technology, Changsha, Hunan 410083, ChinaCollege of Science, National University of Defense Technology, Changsha, Hunan 410083, ChinaSchool of Mathematics and Computer Science, Guangxi University for Nationalities, Nanning, Guangxi 530006, ChinaSchool of Mathematics, Hunan Institute of Science and Technology, Yueyang, Hunan 414006, ChinaWe investigate a nonlinear viscoelastic equation with interior time-varying delay and nonlinear dissipative boundary feedback. Under suitable assumptions on the relaxation function and time-varying delay effect together with nonlinear dissipative boundary feedback, we prove the global existence of weak solutions and asymptotic behavior of the energy by using the Faedo-Galerkin method and the perturbed energy method, respectively. This result improves earlier ones in the literature, such as Kirane and Said-Houari (2011) and Ammari et al. (2010). Moreover, we give an positive answer to the open problem given by Kirane and Said-Houari (2011).http://dx.doi.org/10.1155/2014/102594 |
| spellingShingle | Zaiyun Zhang Jianhua Huang Zhenhai Liu Mingbao Sun Boundary Stabilization of a Nonlinear Viscoelastic Equation with Interior Time-Varying Delay and Nonlinear Dissipative Boundary Feedback Abstract and Applied Analysis |
| title | Boundary Stabilization of a Nonlinear Viscoelastic Equation with Interior Time-Varying Delay and Nonlinear Dissipative Boundary Feedback |
| title_full | Boundary Stabilization of a Nonlinear Viscoelastic Equation with Interior Time-Varying Delay and Nonlinear Dissipative Boundary Feedback |
| title_fullStr | Boundary Stabilization of a Nonlinear Viscoelastic Equation with Interior Time-Varying Delay and Nonlinear Dissipative Boundary Feedback |
| title_full_unstemmed | Boundary Stabilization of a Nonlinear Viscoelastic Equation with Interior Time-Varying Delay and Nonlinear Dissipative Boundary Feedback |
| title_short | Boundary Stabilization of a Nonlinear Viscoelastic Equation with Interior Time-Varying Delay and Nonlinear Dissipative Boundary Feedback |
| title_sort | boundary stabilization of a nonlinear viscoelastic equation with interior time varying delay and nonlinear dissipative boundary feedback |
| url | http://dx.doi.org/10.1155/2014/102594 |
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