Frequency domain approach for the polynomial stability of a system of partially damped wave equations

Zhuangyi Liu; Bopeng Rao

doi:10.1016/j.jmaa.2007.02.021

Frequency domain approach for the polynomial stability of a system of partially damped wave equations

Zhuangyi Liu, Bopeng Rao

Mathematics & Statistics

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Abstract

In this paper, we study the stability of a system of wave equations which are weakly coupled and partially damped. Using a frequency domain approach based on the growth of the resolvent on the imaginary axis, we establish the polynomial energy decay rate for smooth initial data. We show that the behavior of the system is sensitive to the arithmetic property of the ratio of the wave propagation speeds of the two equations.

Original language	English (US)
Pages (from-to)	860-881
Number of pages	22
Journal	Journal of Mathematical Analysis and Applications
Volume	335
Issue number	2
DOIs	https://doi.org/10.1016/j.jmaa.2007.02.021
State	Published - Nov 15 2007

Keywords

Frequency domain
Indirect damping
Polynomial decay rate

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abstract = "In this paper, we study the stability of a system of wave equations which are weakly coupled and partially damped. Using a frequency domain approach based on the growth of the resolvent on the imaginary axis, we establish the polynomial energy decay rate for smooth initial data. We show that the behavior of the system is sensitive to the arithmetic property of the ratio of the wave propagation speeds of the two equations.",

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AU - Liu, Zhuangyi

AU - Rao, Bopeng

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N2 - In this paper, we study the stability of a system of wave equations which are weakly coupled and partially damped. Using a frequency domain approach based on the growth of the resolvent on the imaginary axis, we establish the polynomial energy decay rate for smooth initial data. We show that the behavior of the system is sensitive to the arithmetic property of the ratio of the wave propagation speeds of the two equations.

AB - In this paper, we study the stability of a system of wave equations which are weakly coupled and partially damped. Using a frequency domain approach based on the growth of the resolvent on the imaginary axis, we establish the polynomial energy decay rate for smooth initial data. We show that the behavior of the system is sensitive to the arithmetic property of the ratio of the wave propagation speeds of the two equations.

KW - Frequency domain

KW - Indirect damping

KW - Polynomial decay rate

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Frequency domain approach for the polynomial stability of a system of partially damped wave equations

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Keywords

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