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 (2010)

  • 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 L2 space can be controlled to zero by usual control functions, and every initial datum in L2(Ω) can be controlled to zero using control functions in a weighted L2 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 (2010): 381-408. <http://eudml.org/doc/90735>.

@article{Cannarsa2010,
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 L2 space can be controlled to zero by usual control functions, and every initial datum in L2(Ω) can be controlled to zero using control functions in a weighted L2 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.; weighted observability inequalities},
language = {eng},
month = {3},
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/90735},
volume = {10},
year = {2010},
}

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
DA - 2010/3//
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 L2 space can be controlled to zero by usual control functions, and every initial datum in L2(Ω) can be controlled to zero using control functions in a weighted L2 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.; weighted observability inequalities
UR - http://eudml.org/doc/90735
ER -

References

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