Abstract and Applied Analysis

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

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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).

Article information

Source
Abstr. Appl. Anal., Volume 2014, Special Issue (2014), Article ID 102594, 14 pages.

Dates
First available in Project Euclid: 3 October 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1412360633

Digital Object Identifier
doi:10.1155/2014/102594

Mathematical Reviews number (MathSciNet)
MR3224301

Zentralblatt MATH identifier
07021736

Citation

Zhang, Zaiyun; Huang, Jianhua; Liu, Zhenhai; Sun, Mingbao. Boundary Stabilization of a Nonlinear Viscoelastic Equation with Interior Time-Varying Delay and Nonlinear Dissipative Boundary Feedback. Abstr. Appl. Anal. 2014, Special Issue (2014), Article ID 102594, 14 pages. doi:10.1155/2014/102594. https://projecteuclid.org/euclid.aaa/1412360633


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