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Z. Naturforsch. 69a, 547 – 552 (2014)
doi:10.5560/ZNA.2014-0047
Exponential Stability of the Energy of the Wave Equation with Variable Coefficients and a Boundary Distributed Delay
Wenjun Liu
College of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing 210044, China
Received January 19, 2014 / revised June 7, 2014 / published online July 30, 2014
Reprint requests to: W. L.; E-mail: wjliu@nuist.edu.cn
In this paper, we consider a wave equation with space variable coefficients. Due to physical considerations, a distributed delay damping is acted on the part of the boundary. Under suitable assumptions, we prove the exponential stability of the energy based on the use of Riemannian geometry method, the perturbed energy argument, and some observability inequalities. From the applications point of view, our results may provide some qualitative analysis and intuition for the researchers in fields such as engineering, biophysics, and mechanics. And the method is rather general and can be adapted to other evolution systems with variable coefficients (e. g. elasticity plates) as well.
Key words: Wave Equation; Variable Coefficients; Stabilization; Distributed Delay.
PACS numbers: 02.30.Ks; 04.30.Db; 05.45.Gg
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