Electron. J. Differential Equations, Vol. 2017 (2017), No. 198, pp. 1-14.

Stabilization of wave equations with variable coefficient and delay in the dynamical boundary feedback

Dandan Guo, Zhifei Zhang

Abstract:
In this article we consider the boundary stabilization of a wave equation with variable coefficients. This equation has an acceleration term and a delayed velocity term on the boundary. Under suitable geometric conditions, we obtain the exponential decay for the solutions. Our proof relies on the geometric multiplier method and the Lyapunov approach.

Submitted June 13, 2017. Published August 9, 2017.
Math Subject Classifications: 35N25, 39A30.
Key Words: Difference scheme; inverse elliptic problem; stability; overdetermination; nonlocal problem.

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Dandan Guo
School of Mathematics and Statistics
Huazhong University of Science and Technology
Wuhan 430074, China
email: m201570062@hust.edu.cn
Zhifei Zhang
School of Mathematics and Statistics
Huazhong University of Science and Technology
Wuhan 430074, China
zhangzf@hust.edu.cn

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