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

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  • Zaiyun Zhang
  • Jianhua Huang
  • Zhenhai Liu
  • Mingbao Sun

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).

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Handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:102594
DOI: 10.1155/2014/102594
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