Spectral analysis and stabilization of a coupled wave-ODE system
Spectral analysis and stabilization of a coupled wave-ODE system
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DOI：
10.1007/s11424-014-2219-5
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发表时间：
2014-06
影响因子：
2.1
通讯作者：
Dong‐xia Zhao;Jun‐min Wang
中科院分区：
文献类型：
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作者：
Dong‐xia Zhao;Jun‐min Wang
本文考虑了波动方程中具有K-V阻尼项和常微分方程组中存在未知参数的互联波-微分方程组。结果表明，系统算符的谱由两部分组成：点谱和连续谱。连续谱由一个孤立点组成，且渐近本征值有两个分支：第一个分支向−∞累加，另一个分支趋向于Lorn。证明了存在一个广义本征函数序列，它构成了Hilbert状态空间的Riesz基。由此，得出了系统的谱决定增长条件和指数稳定性。
In this paper, an interconnected wave-ODE system with K-V damping in the wave equation and unknown parameters in the ODE is considered. It is found that the spectrum of the system operator is composed of two parts: Point spectrum and continuous spectrum. The continuous spectrum consists of an isolated point, and there are two branches of the asymptotic eigenvalues: The first branch is accumulating towards, and the other branch tends to −∞. It is shown that there is a sequence of generalized eigenfunctions, which forms a Riesz basis for the Hilbert state space. As a consequence, the spectrum-determined growth condition and exponential stability of the system are concluded.