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

Abstract

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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 : = ∪ 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.

How to cite

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Cannarsa, 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 -

References

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