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Stability and instability of the damped inhomogeneous and anisotropic elastic wave equation with a memory
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  • Yongli Xing,
  • Fengyan Yang,
  • Zihui Liu,
  • Zhenhu Ning
Yongli Xing
China University of Geosciences Beijing
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Fengyan Yang
Beijing Forestry University

Corresponding Author:yangfy16@bjfu.edu.cn

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Zihui Liu
China University of Geosciences Beijing
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Zhenhu Ning
Beijing University of Technology
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Abstract

We consider the damped inhomogeneous and anisotropic elastic wave equation with a memory on bounded domain. We apply the Morawetz estimates and the compactness-uniqueness arguments to prove the stability results. We also give a discussion of the instability of the system when the proposed condition is not satisfied.