# American Institute of Mathematical Sciences

October  2016, 21(8): 2491-2507. doi: 10.3934/dcdsb.2016057

## Stabilization of the wave equation with interior input delay and mixed Neumann-Dirichlet boundary

 1 College of Science, Civil Aviation University of China, Tianjin 300300, China 2 Department of Mathematics, Tianjin University, Tianjin 300072, China, China

Received  October 2015 Revised  April 2016 Published  September 2016

This paper considers the stabilization of a wave equation with interior input delay: $\mu_1u(x,t)+\mu_2u(x,t-\tau)$, where $u(x,t)$ is the control input. A new dynamic feedback control law is obtained to stabilize the closed-loop system exponentially for any time delay $\tau>0$ provided that $|\mu_1|\neq|\mu_2|$. Moreover, some sufficient conditions are given for discriminating the asymptotic stability and instability of the closed-loop system.
Citation: Yanni Guo, Genqi Xu, Yansha Guo. Stabilization of the wave equation with interior input delay and mixed Neumann-Dirichlet boundary. Discrete & Continuous Dynamical Systems - B, 2016, 21 (8) : 2491-2507. doi: 10.3934/dcdsb.2016057
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