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Advances in Mathematical Physics
Volume 2014 (2014), Article ID 735341, 6 pages
http://dx.doi.org/10.1155/2014/735341
Research Article

Stabilization of the Wave Equation with Boundary Time-Varying Delay

1School of Ocean Sciences, China University of Geosciences, Beijing 100083, China
2Institute of Information Engineering, Chinese Academy of Sciences, Beijing 100093, China
3School of Information Engineering, China University of Geosciences, Beijing 100083, China

Received 18 October 2013; Revised 10 January 2014; Accepted 10 January 2014; Published 26 February 2014

Academic Editor: Wen-Xiu Ma

Copyright © 2014 Hao Li 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 study the stabilization of the wave equation with variable coefficients in a bounded domain and a time-varying delay term in the time-varying, weakly nonlinear boundary feedbacks. By the Riemannian geometry methods and a suitable assumption of nonlinearity, we obtain the uniform decay of the energy of the closed loop system.