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Internal Observability, Controllability and Stabilization of the Inhomogeneous and Anisotropic Elastic Wave Equation

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Abstract

In this paper, we consider the inhomogeneous and anisotropic elastic wave equation on bounded domain. We prove the internal observability, controllability and stabilization of the elastic wave equation under a suitable condition of inhomogeneous and anisotropic medias. The main methods are multiplier methods and compactness-uniqueness arguments.

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Acknowledgements

The authors would like to thank the referee and editor for their very helpful comments and suggestions.

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Authors and Affiliations

  1. School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing, 100049, People’s Republic of China

    Yusen Meng

  2. Key Laboratory of Systems and Control, Institute of Systems Science, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, People’s Republic of China

    Yusen Meng

  3. Faculty of Information Technology, Beijing University of Technology, Beijing, 100124, People’s Republic of China

    Zhen-Hu Ning

  4. School of Sciences, Beijing Forestry University, Beijing, 100083, People’s Republic of China

    Fengyan Yang

Authors
  1. Yusen Meng
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  2. Zhen-Hu Ning
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  3. Fengyan Yang
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Correspondence to Fengyan Yang.

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This work is supported by the National Natural Science Foundation of China under Grant No. 61573342 and the Key Research Program of Frontier Sciences, CAS, No. QYZDJ-SSW-SYS011.

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Meng, Y., Ning, ZH. & Yang, F. Internal Observability, Controllability and Stabilization of the Inhomogeneous and Anisotropic Elastic Wave Equation. Appl Math Optim 84, 1605–1621 (2021). https://doi.org/10.1007/s00245-020-09688-x

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