# Controls insensitizing the norm of the solution of a semilinear heat equation in unbounded domains

ESAIM: Control, Optimisation and Calculus of Variations (2010)

- Volume: 2, page 125-149
- ISSN: 1292-8119

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topde Teresa, L.. "Controls insensitizing the norm of the solution of a semilinear heat equation in unbounded domains." ESAIM: Control, Optimisation and Calculus of Variations 2 (2010): 125-149. <http://eudml.org/doc/197307>.

@article{deTeresa2010,

abstract = {
We consider a semilinear heat equation in an unbounded
domain Ω with partially known initial data. The insensitizing problem
consists in finding a control function such that some functional of the
state is locally insensitive to the perturbations of these initial data. For
bounded domains Bodart and Fabre proved the existence of insensitizing controls of the norm of the observation of the solution in an open
subset of the domain. In this paper we prove similar results when Ω is
unbounded. We consider the problem in bounded domains of the form
Ωr = Ω ∩ Br where Br denotes the ball centered in zero of radius r We
show that for r large enough the control proposed by Bodart and Fabre
for the problem in Ωr, provides an insensitizing control for our problem
in Ω.
},

author = {de Teresa, L.},

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

keywords = {Heat equation / insensitizing control / unbounded domains.; heat equation; parabolic semilinear system; insensitizing control},

language = {eng},

month = {3},

pages = {125-149},

publisher = {EDP Sciences},

title = {Controls insensitizing the norm of the solution of a semilinear heat equation in unbounded domains},

url = {http://eudml.org/doc/197307},

volume = {2},

year = {2010},

}

TY - JOUR

AU - de Teresa, L.

TI - Controls insensitizing the norm of the solution of a semilinear heat equation in unbounded domains

JO - ESAIM: Control, Optimisation and Calculus of Variations

DA - 2010/3//

PB - EDP Sciences

VL - 2

SP - 125

EP - 149

AB -
We consider a semilinear heat equation in an unbounded
domain Ω with partially known initial data. The insensitizing problem
consists in finding a control function such that some functional of the
state is locally insensitive to the perturbations of these initial data. For
bounded domains Bodart and Fabre proved the existence of insensitizing controls of the norm of the observation of the solution in an open
subset of the domain. In this paper we prove similar results when Ω is
unbounded. We consider the problem in bounded domains of the form
Ωr = Ω ∩ Br where Br denotes the ball centered in zero of radius r We
show that for r large enough the control proposed by Bodart and Fabre
for the problem in Ωr, provides an insensitizing control for our problem
in Ω.

LA - eng

KW - Heat equation / insensitizing control / unbounded domains.; heat equation; parabolic semilinear system; insensitizing control

UR - http://eudml.org/doc/197307

ER -

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