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		Yuqing YAN,Yi ZHAO,Yu HUANG.[en_title][J].Control Theory and Technology,2009,7(1):73~.[Copy]

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YuqingYAN,YiZHAO,YuHUANG
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Received:September 10, 2006Revised:December 28, 2007

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The cost of approximate controllability for semilinear heat equations

Yuqing YAN, Yi ZHAO, Yu HUANG

(Department of Mathematics, Sun Yat-Sen University, Guangzhou Guangdong 510275, China)

Abstract:

We consider the semilinear heat equation with globally Lipschitz non-linearity involving gradient termsin a bounded domain of Rn. In this paper, we obtain explicit bounds of the cost of approximate controllability, i.e., of the minimal norm of a control needed to control the system approximately. The methods we used combine global Carleman estimates, the variational approach to approximate controllability and Schauder’s fixed point theorem.

Key words: Cost Approximate controllability Semilinear heat equation