Null controllability of the heat equation in unbounded domains by a finite measure control region

Piermarco Cannarsa, Patrick Martinez, Judith Vancostenoble
2004 E S A I M: Control, Optimisation and Calculus of Variations  
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, we prove two null controllability results: under some technical assumption on the control parts ωn, we prove that every initial datum in some weighted L 2 space can be controlled to zero by usual control functions, and every initial
more » ... 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. Mathematics Subject Classification. 35K05, 93B05, 93B07.
doi:10.1051/cocv:2004010 fatcat:5w7twtwdkvfbtiffue3tvhv3eq