# 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

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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 (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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