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^*

^*此作品的通讯作者

数学学院

Université Paris-Saclay

科研成果: 期刊稿件 › 文章 › 同行评审

4 引用（Scopus）

摘要

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.

源语言	英语
文章编号	715
期刊	Mathematics
卷	8
期	5
DOI	https://doi.org/10.3390/MATH8050715
出版状态	已出版 - 1 5月 2020

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10.3390/MATH8050715

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title = "Logarithmic decay of wave equation with Kelvin-Voigt Damping",

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.",

keywords = "Carleman estimate, Kelvin-Voigt damping, Logarithmic stability, Wave equation",

author = "Luc Robbiano and Qiong Zhang",

note = "Publisher Copyright: {\textcopyright} 2020 by the authors.",

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AU - Zhang, Qiong

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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.

KW - Carleman estimate

KW - Kelvin-Voigt damping

KW - Logarithmic stability

KW - Wave equation

UR - https://www.scopus.com/pages/publications/85085529994

U2 - 10.3390/MATH8050715

DO - 10.3390/MATH8050715

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SN - 2227-7390

VL - 8

JO - Mathematics

JF - Mathematics

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Logarithmic decay of wave equation with Kelvin-Voigt Damping

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