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Null controllability of the heat equationin unbounded domainsby a finite measure control region

Published online by Cambridge University Press:  15 June 2004

Piermarco Cannarsa ,
Patrick Martinez  and
Judith Vancostenoble
Piermarco Cannarsa
Affiliation:
Dipartimento di Matematica, Università di Roma “Tor Vergata”, Via della Ricerca Scientifica, 00133 Roma, Italy; [email protected].
Patrick Martinez
Affiliation:
Laboratoire M.I.P., UMR CNRS 5640, Université Paul Sabatier Toulouse III, 118 route de Narbonne, 31062 Toulouse Cedex 4, France; [email protected].; [email protected].
Judith Vancostenoble
Affiliation:
Laboratoire M.I.P., UMR CNRS 5640, Université Paul Sabatier Toulouse III, 118 route de Narbonne, 31062 Toulouse Cedex 4, France; [email protected].; [email protected].
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Abstract

Motivated by two recent works of Micu and Zuazua and Cabanillas, De Menezes and Zuazua, we study the null controllability of the heat equationin unbounded domains, typically $\mathbb R_+$ or  $\mathbb R^N$ . Considering an unbounded and disconnected control region of the form $\omega := \cup _n \omega _n$ , we prove two null controllability results:under some technical assumption on the control parts $\omega _n$ , we provethat 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 usingcontrol 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.

Keywords

Null controllabilityweighted observability inequalities.
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 10 , Issue 3 , July 2004 , pp. 381 - 408
Copyright
© EDP Sciences, SMAI, 2004

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