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Open AccessArticle

Logarithmic Decay of Wave Equation with Kelvin-Voigt Damping

by 1 and 2,*
1
Laboratoire de Mathématiques Appliquées, UMR 8100 du CNRS, Université Paris–Saclay (site UVSQ), 45 avenue des Etats Unis, 78035 Versailles, France
2
School of Mathematics and Statistics, Beijing Key Laboratory on MCAACI, Beijing Institute of Technology, Beijing 100081, China
*
Author to whom correspondence should be addressed.
Mathematics 2020, 8(5), 715; https://doi.org/10.3390/math8050715
Received: 2 April 2020 / Revised: 22 April 2020 / Accepted: 25 April 2020 / Published: 3 May 2020
(This article belongs to the Special Issue Modern Analysis and Partial Differential Equation)
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. View Full-Text
Keywords: Carleman estimate; wave equation; Kelvin-Voigt damping; logarithmic stability Carleman estimate; wave equation; Kelvin-Voigt damping; logarithmic stability
MDPI and ACS Style

Robbiano, L.; Zhang, Q. Logarithmic Decay of Wave Equation with Kelvin-Voigt Damping. Mathematics 2020, 8, 715. https://doi.org/10.3390/math8050715

AMA Style

Robbiano L, Zhang Q. Logarithmic Decay of Wave Equation with Kelvin-Voigt Damping. Mathematics. 2020; 8(5):715. https://doi.org/10.3390/math8050715

Chicago/Turabian Style

Robbiano, Luc; Zhang, Qiong. 2020. "Logarithmic Decay of Wave Equation with Kelvin-Voigt Damping" Mathematics 8, no. 5: 715. https://doi.org/10.3390/math8050715

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