On well-posedness, regularity and exact controllability for problems of transmission of plate equation with variable coefficients

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	On well-posedness, regularity and exact controllability for problems of transmission of plate equation with variable coefficients
	Guo, Bao-Zhu1,2 ; Shao, Zhi-Chao 2
	2007-12-01
发表期刊	QUARTERLY OF APPLIED MATHEMATICS
ISSN	0033-569X
卷号	65 期号:4 页码:705-736
摘要	A system of transmission of Euler-Bernoulli plate equation with variable coefficients under Neumann control and collocated observation is studied. Using the multiplier method on a Riemannian manifold, it is shown that the system is well-posed in the sense of D. Salamon. This establishes the equivalence between the exact controllability of an open-loop system and the exponential stability of a closed-loop system under the proportional output feedback. The regularity of the system in the sense of G. Weiss is also proved, and the feedthrough operator is found to be zero. These properties make this PDE system parallel in many ways to the finite-dimensional ones. Finally, the exact controllability of an open-loop system is developed under a uniqueness assumption by establishing the observability inequality for the dual system.
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000251628800005
出版者	AMER MATHEMATICAL SOC
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/5057
专题	系统科学研究所
通讯作者	Guo, Bao-Zhu
作者单位	1.Acad Sinica, Acad Math & Syst Sci, Beijing 100080, Peoples R China 2.Univ Witwatersrand, Sch Computat & Appl Math, ZA-2050 Wits, South Africa
推荐引用方式 GB/T 7714	Guo, Bao-Zhu,Shao, Zhi-Chao. On well-posedness, regularity and exact controllability for problems of transmission of plate equation with variable coefficients[J]. QUARTERLY OF APPLIED MATHEMATICS,2007,65(4):705-736.
APA	Guo, Bao-Zhu,&Shao, Zhi-Chao.(2007).On well-posedness, regularity and exact controllability for problems of transmission of plate equation with variable coefficients.QUARTERLY OF APPLIED MATHEMATICS,65(4),705-736.
MLA	Guo, Bao-Zhu,et al."On well-posedness, regularity and exact controllability for problems of transmission of plate equation with variable coefficients".QUARTERLY OF APPLIED MATHEMATICS 65.4(2007):705-736.