In this article we consider the boundary stabilization of the wave equation with variable coefficients and a dynamical Neumann boundary control. The dynamics on the boundary comes from the acceleration terms which can not be ignored in some physical applications. It has been known that addition of dynamics to the boundary may change drastically the stability properties of the underlying system. In this paper by applying a boundary feedback control we obtain the exponential decay for the solutions. Our proof relies on the Geometric multiplier skills and the energy perturbed approach.
Submitted December 9, 2015. Published January 15, 2016.
Math Subject Classifications: 34H05, 35L05, 49K25, 93C20, 93D15.
Key Words: Exponential decay; wave equation with variable coefficients; dynamical boundary control.
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| Zhifei Zhang |
Department of Mathematics
Huazhong University of Science and Technology
Wuhan, 430074, China
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