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

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• 作者：Zhuangyi Liu ; Bopeng Rao
• 关键词：Indirect damping ; Polynomial decay rate ; Frequency domain
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2007
• 出版时间：15 November 2007
• 年：2007
• 卷：335
• 期：2
• 页码：860-881
• 全文大小：205 K

文摘

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.