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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| Summary: | 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). |
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| ISSN: | 1085-3375 1687-0409 |