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Abstract and Applied Analysis
Volume 2014, Article ID 102594, 14 pages
http://dx.doi.org/10.1155/2014/102594
Research Article

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

1College of Science, National University of Defense Technology, Changsha, Hunan 410083, China
2School of Mathematics, Hunan Institute of Science and Technology, Yueyang, Hunan 414006, China
3School of Mathematics and Computer Science, Guangxi University for Nationalities, Nanning, Guangxi 530006, China

Received 22 January 2014; Revised 2 May 2014; Accepted 16 May 2014; Published 9 June 2014

Academic Editor: Chuangxia Huang

Copyright © 2014 Zaiyun Zhang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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).