Logarithmic decay of wave equation with Kelvin-Voigt Damping

Luc Robbiano; Qiong Zhang

doi:10.3390/MATH8050715

Logarithmic decay of wave equation with Kelvin-Voigt Damping

Luc Robbiano, Qiong Zhang^*

^*Corresponding author for this work

School of Mathematics and Statistics

Université Paris-Saclay

Research output: Contribution to journal › Article › peer-review

4 Citations (Scopus)

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.

Original language	English
Article number	715
Journal	Mathematics
Volume	8
Issue number	5
DOIs	https://doi.org/10.3390/MATH8050715
Publication status	Published - 1 May 2020

Keywords

Carleman estimate
Kelvin-Voigt damping
Logarithmic stability
Wave equation

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10.3390/MATH8050715

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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.",

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N2 - 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.

AB - 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.

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KW - Kelvin-Voigt damping

KW - Logarithmic stability

KW - Wave equation

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Logarithmic decay of wave equation with Kelvin-Voigt Damping

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Keywords

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