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Logarithmic Decay of Wave Equation with Kelvin-Voigt Damping

Author

Listed:
  • Luc Robbiano

    (Laboratoire de Mathématiques Appliquées, UMR 8100 du CNRS, Université Paris–Saclay (site UVSQ), 45 avenue des Etats Unis, 78035 Versailles, France)

  • Qiong Zhang

    (School of Mathematics and Statistics, Beijing Key Laboratory on MCAACI, Beijing Institute of Technology, Beijing 100081, China)

Abstract

In this paper, we analyze the longtime behavior of the wave equation with local Kelvin-Voigt Damping. Through introducing proper class symbol and pseudo-diff-calculus, we obtain a Carleman estimate, and then establish an estimate on the corresponding resolvent operator. As a result, we show the logarithmic decay rate for energy of the system without any geometric assumption on the subdomain on which the damping is effective.

Suggested Citation

  • Luc Robbiano & Qiong Zhang, 2020. "Logarithmic Decay of Wave Equation with Kelvin-Voigt Damping," Mathematics, MDPI, vol. 8(5), pages 1-19, May.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:5:p:715-:d:353633
    as

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    References listed on IDEAS

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    1. ,, 2003. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 19(4), pages 691-705, August.
    2. ,, 2003. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 19(1), pages 225-228, February.
    3. ,, 2003. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 19(5), pages 879-883, October.
    4. ,, 2003. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 19(2), pages 411-413, April.
    5. ,, 2003. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 19(6), pages 1195-1198, December.
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    Cited by:

    1. Zhen-Wei Li & Wen-Biao Gao & Bing-Zhao Li, 2020. "The Solvability of a Class of Convolution Equations Associated with 2D FRFT," Mathematics, MDPI, vol. 8(11), pages 1-12, November.

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