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

de 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 -