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
刊名	QUARTERLY OF APPLIED MATHEMATICS
	2007-12-01
卷号	65 期号:4 页码:705-736
ISSN号	0033-569X
英文摘要	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.
WOS研究方向	Mathematics
语种	英语
出版者	AMER MATHEMATICAL SOC
WOS记录号	WOS:000251628800005
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/5056]
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.