L^p and L~∞ Norm Estimates of the Cost of the Controllability for Heat Equations

L^p and L~∞ Norm Estimates of the Cost of the Controllability for Heat Equations

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摘要 This paper is concerned with the bound of the cost of approximate controllability and null controllability of heat equations, i.e., the minimal Lp norm and L∞ norm of a control needed to control the system approximately or a control needed to steer the state of the system to zero. The methods we use combine observability inequalities, energy estimates for heat equations and the dual theory. This paper is concerned with the bound of the cost of approximate controllability and null controllability of heat equations, i.e., the minimal Lp norm and L∞ norm of a control needed to control the system approximately or a control needed to steer the state of the system to zero. The methods we use combine observability inequalities, energy estimates for heat equations and the dual theory.

作者 Pei Dong LEI Xu LIU Hang GAO

机构地区 School of Mathematics & Statistics

出处《Acta Mathematica Sinica,English Series》 SCIE CSCD 2009年第8期1305-1324,共20页 数学学报（英文版）

基金 Supported by Key Project of Chinese Ministry of Education (No. i08046) National Natural Science Foundation of China (Nos. 10601010,10471021) Grant NENU-STC07007

关键词 approximate controllability null controllability cost of the controllability observability inequality approximate controllability, null controllability, cost of the controllability, observability inequality

分类号 TP273 [自动化与计算机技术—检测技术与自动化装置] TH122 [机械工程—机械设计及理论]

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Acta Mathematica Sinica,English Series

2009年第8期

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L^p and L~∞ Norm Estimates of the Cost of the Controllability for Heat Equations

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