NULL CONTROLLABILITY OF THE HEAT EQUATION IN UNBOUNDED DOMAINS BY A FINITE MEASURE CONTROL REGION
NULL CONTROLLABILITY OF THE HEAT EQUATION IN UNBOUNDED DOMAINS BY A FINITE MEASURE CONTROL REGION
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DOI：
10.1051/cocv:2004010
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发表时间：
2004-07
期刊：
影响因子：
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通讯作者：
P. Cannarsa;P. Martinez;J. Vancostenoble
中科院分区：
文献类型：
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作者：
P. Cannarsa;P. Martinez;J. Vancostenoble
受Micu和Zuazua以及Cabanillas， De Menezes和Zuazua最近的两项工作的启发，我们研究了无界区域（通常是R+或R n）中热方程的零可控性。考虑一个形式为ω:=∪nωn的无界非连续控制区，我们证明了两个零可控性结果：在控制部分Ω n的一些技术假设下，我们证明了在某一加权l2空间中的每一个初始基准都可以用通常的控制函数控制为零，并且在某一加权l2空间中的每一个初始基准（Ω）都可以用控制函数控制为零。最后给出了控制区域具有有限测度的几个例子
Motivated by two recent works of Micu and Zuazua and Cabanillas, De Menezes and Zuazua, we study the null controllability of the heat equation in unbounded domains, typically R+ or R N. Considering an unbounded and disconnected control region of the form ω := ∪nωn ,w e prove two null controllability results: under some technical assumption on the control parts ωn ,w e prove that every initial datum in some weighted L 2 space can be controlled to zero by usual control functions, and every initial datum in L 2 (Ω) can be controlled to zero using control functions in a weighted L 2 space. At last we give several examples in which the control region has a finite measure and our