This paper is concerned with the controllability of some (linear and semilinear) non-diagonalizable parabolic systems of PDEs. We will show that the well known null controllability properties of the classical heat equation are also satisfied by these systems at least when there are as many scalar controls as equations and some (maybe technical) conditions are satisfied. We will also show that, in some particular situations, the number of controls can be reduced. The minimal amount is then determined by a Kalman rank condition.
DOI : 10.1051/cocv/2014063
Mots clés : Null controllability, parabolic, non-diagonalizable
@article{COCV_2015__21_4_1178_0,
author = {Fern\'andez-Cara, Enrique and Gonz\'alez-Burgos, Manuel and de Teresa, Luz},
title = {Controllability of linear and semilinear non-diagonalizable parabolic systems},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
pages = {1178--1204},
publisher = {EDP-Sciences},
volume = {21},
number = {4},
year = {2015},
doi = {10.1051/cocv/2014063},
mrnumber = {3395760},
zbl = {1320.93017},
language = {en},
url = {http://archive.numdam.org/articles/10.1051/cocv/2014063/}
}
TY - JOUR AU - Fernández-Cara, Enrique AU - González-Burgos, Manuel AU - de Teresa, Luz TI - Controllability of linear and semilinear non-diagonalizable parabolic systems JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2015 SP - 1178 EP - 1204 VL - 21 IS - 4 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/cocv/2014063/ DO - 10.1051/cocv/2014063 LA - en ID - COCV_2015__21_4_1178_0 ER -
%0 Journal Article %A Fernández-Cara, Enrique %A González-Burgos, Manuel %A de Teresa, Luz %T Controllability of linear and semilinear non-diagonalizable parabolic systems %J ESAIM: Control, Optimisation and Calculus of Variations %D 2015 %P 1178-1204 %V 21 %N 4 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/cocv/2014063/ %R 10.1051/cocv/2014063 %G en %F COCV_2015__21_4_1178_0
Fernández-Cara, Enrique; González-Burgos, Manuel; de Teresa, Luz. Controllability of linear and semilinear non-diagonalizable parabolic systems. ESAIM: Control, Optimisation and Calculus of Variations, Tome 21 (2015) no. 4, pp. 1178-1204. doi : 10.1051/cocv/2014063. http://archive.numdam.org/articles/10.1051/cocv/2014063/
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