a1 Dipartimento di Matematica, Università di Roma “Tor Vergata”, Via della Ricerca Scientifica, 00133 Roma, Italy; email@example.com.
a2 Laboratoire M.I.P., UMR CNRS 5640, Université Paul Sabatier Toulouse III, 118 route de Narbonne, 31062 Toulouse Cedex 4, France; firstname.lastname@example.org.; email@example.com.
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 . Considering an unbounded and disconnected control region of the form , we prove two null controllability results: under some technical assumption on the control parts , 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.
(Received May 20 2002)
(Revised July 18 2003)
(Online publication June 15 2004)
Mathematics Subject Classification: