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

Piermarco Cannarsa; Patrick Martinez; Judith Vancostenoble

ESAIM: Control, Optimisation and Calculus of Variations (2004)

- Volume: 10, Issue: 3, page 381-408
- ISSN: 1292-8119

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topCannarsa, Piermarco, Martinez, Patrick, and Vancostenoble, Judith. "Null controllability of the heat equation in unbounded domains by a finite measure control region." ESAIM: Control, Optimisation and Calculus of Variations 10.3 (2004): 381-408. <http://eudml.org/doc/244748>.

@article{Cannarsa2004,

abstract = {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 $\mathbb \{R\}_+$ 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 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 $L^2 (\Omega )$ 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.},

author = {Cannarsa, Piermarco, Martinez, Patrick, Vancostenoble, Judith},

journal = {ESAIM: Control, Optimisation and Calculus of Variations},

keywords = {null controllability; weighted observability inequalities; Null controllability},

language = {eng},

number = {3},

pages = {381-408},

publisher = {EDP-Sciences},

title = {Null controllability of the heat equation in unbounded domains by a finite measure control region},

url = {http://eudml.org/doc/244748},

volume = {10},

year = {2004},

}

TY - JOUR

AU - Cannarsa, Piermarco

AU - Martinez, Patrick

AU - Vancostenoble, Judith

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

JO - ESAIM: Control, Optimisation and Calculus of Variations

PY - 2004

PB - EDP-Sciences

VL - 10

IS - 3

SP - 381

EP - 408

AB - 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 $\mathbb {R}_+$ 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 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 $L^2 (\Omega )$ 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.

LA - eng

KW - null controllability; weighted observability inequalities; Null controllability

UR - http://eudml.org/doc/244748

ER -

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