RECENT PROGRESS ON C ONTROLLABILITY/OBSERVABILITY FOR SYSTEMS GOVERNED BY PARTIAL DIFFERENTIAL EQUATIONS

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	RECENT PROGRESS ON C ONTROLLABILITY/OBSERVABILITY FOR SYSTEMS GOVERNED BY PARTIAL DIFFERENTIAL EQUATIONS
其他题名	RECENT PROGRESS ON C ONTROLLABILITY/OBSERVABILITY FOR SYSTEMS GOVERNED BY PARTIAL DIFFERENTIAL EQUATIONS
	Li Hongheng 1; Lu Qi 1; Zhang Xu 2
	2010
发表期刊	系统科学与复杂性：英文版
ISSN	1009-6124
卷号	000 期号:003 页码:527-545
摘要	The main purpose of this paper is to overview some recent methods and results on controllability/observability problems for systems governed by partial differential equations. First, the authors review the theory for linear partial differential equations, including the iteration method for the null controllability of the time-invariant heat equation and the Rellich-type multiplier method for the exact controllability of the time-invariant wave equation, and especially a unified controllability/observability theory for parabolic and hyperbolic equations based on a global Carleman estimate. Then, the authors present sharp global controllability results for both semi-linear parabolic and hyperbolic equations, based on linearization approach, sharp observability estimates for the corresponding linearized systems and the fixed point argument. Finally, the authors survey the local null controllability result for a class of quasilinear parabolic equations based on the global Carleman estimate, and the local exact controllability result for general hyperbolic equations based on a new unbounded perturbation techniaue.
其他摘要	The main purpose of this paper is to overview some recent methods and results on controllability/observability problems for systems governed by partial differential equations. First, the authors review the theory for linear partial differential equations, including the iteration method for the null controllability of the time-invariant heat equation and the Rellich-type multiplier method for the exact controllability of the time-invariant wave equation, and especially a unified controllability/observability theory for parabolic and hyperbolic equations based on a global Carleman estimate. Then, the authors present sharp global controllability results for both semi-linear parabolic and hyperbolic equations, based on linearization approach, sharp observability estimates for the corresponding linearized systems and the fixed point argument. Finally, the authors survey the local null controllability result for a class of quasilinear parabolic equations based on the global Carleman estimate, and the local exact controllability result for general hyperbolic equations based on a new unbounded perturbation techniaue.
关键词	非线性偏微分方程线性系统 Carleman 拟线性抛物型方程精确可控性双曲方程线性化方法波动方程
收录类别	CSCD
语种	中文
CSCD记录号	CSCD:4077043
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/56423
专题	中国科学院数学与系统科学研究院
作者单位	1.四川大学 2.中国科学院数学与系统科学研究院
推荐引用方式 GB/T 7714	Li Hongheng,Lu Qi,Zhang Xu. RECENT PROGRESS ON C ONTROLLABILITY/OBSERVABILITY FOR SYSTEMS GOVERNED BY PARTIAL DIFFERENTIAL EQUATIONS[J]. 系统科学与复杂性：英文版,2010,000(003):527-545.
APA	Li Hongheng,Lu Qi,&Zhang Xu.(2010).RECENT PROGRESS ON C ONTROLLABILITY/OBSERVABILITY FOR SYSTEMS GOVERNED BY PARTIAL DIFFERENTIAL EQUATIONS.系统科学与复杂性：英文版,000(003),527-545.
MLA	Li Hongheng,et al."RECENT PROGRESS ON C ONTROLLABILITY/OBSERVABILITY FOR SYSTEMS GOVERNED BY PARTIAL DIFFERENTIAL EQUATIONS".系统科学与复杂性：英文版 000.003(2010):527-545.