Boundary Stabilization of a Nonlinear Viscoelastic Equation with Interior Time-Varying Delay and Nonlinear Dissipative Boundary Feedback

Zaiyun Zhang, Jianhua Huang, Zhenhai Liu and Mingbao Sun

Abstract and Applied Analysis, 2014, vol. 2014, 1-14

Abstract:

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).

Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:102594

DOI: 10.1155/2014/102594

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