Electron. J. Differential Equations, Vol. 2018 (2018), No. 160, pp. 1-19.

Stabilization of wave equations with variable coefficients and internal memory

Zhen-Hu Ning, Fengyan Yang

In this article, we consider the stabilization of a wave equation with variable coefficients and internal memory in an open bounded domain, by the Riemannian geometry approach. For the wave equation with a locally distributed memory with a kernel, we obtain exponential decay of the energy under some geometric conditions. In addition, for the wave equation with nonlinear internal time-varying delay without upper bound, we obtain uniform decay of the energy.

Submitted July 21, 2018. Published September 5, 2018.
Math Subject Classifications: 93C20, 93D20.
Key Words: Stabilization; wave equation with variable coefficients; memory term; time-varying delay; geometric conditions.

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Zhen-Hu Ning
Faculty of Information Technology
Beijing University of Technology
Beijing 100124, China
email: ningzhenhu@bjut.edu.cn
Fengyan Yang
Key Laboratory of Systems and Control
Institute of Systems Science
Academy of Mathematics and Systems Science
Chinese Academy of Sciences, Beijing 100190, China
email: yangfengyan12@mails.ucas.ac.cn

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