Null controllability of the heat equation in unbounded domains by a finite measure control region
ESAIM: Control, Optimisation and Calculus of Variations, Tome 10 (2004) no. 3, pp. 381-408.

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 + or N . Considering an unbounded and disconnected control region of the form ω:= n ω n , we prove two null controllability results: under some technical assumption on the control parts ω n , we 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 null controllability results apply.

DOI : 10.1051/cocv:2004010
Classification : 35K05, 93B05, 93B07
Mots clés : null controllability, weighted observability inequalities
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     title = {Null controllability of the heat equation in unbounded domains by a finite measure control region},
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Cannarsa, Piermarco; Martinez, Patrick; Vancostenoble, Judith. Null controllability of the heat equation in unbounded domains by a finite measure control region. ESAIM: Control, Optimisation and Calculus of Variations, Tome 10 (2004) no. 3, pp. 381-408. doi : 10.1051/cocv:2004010. http://www.numdam.org/articles/10.1051/cocv:2004010/

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