Geodesic
Controllability of linear and semilinear non-diagonalizable parabolic systems
Fernández-Cara, Enrique1  ; González-Burgos, Manuel1  ; de Teresa, Luz2
1 Dpto, E.D.A.N., Universidad de Sevilla, Aptdo. 1160, 41080 Sevilla, Spain
2 Instituto de Matemáticas, Universidad Nacional Autónoma de México, Circuito Exterior, C.U. 04510 D.F. México, Mexico
ESAIM: Control, Optimisation and Calculus of Variations, Tome 21 (2015) no. 4, pp. 1178-1204

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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.

Reçu le :
DOI : 10.1051/cocv/2014063
Classification : 93B05, 35K20
Keywords: Null controllability, parabolic, non-diagonalizable

Fernández-Cara, Enrique 1 ; González-Burgos, Manuel 1 ; de Teresa, Luz 2

1 Dpto, E.D.A.N., Universidad de Sevilla, Aptdo. 1160, 41080 Sevilla, Spain
2 Instituto de Matemáticas, Universidad Nacional Autónoma de México, Circuito Exterior, C.U. 04510 D.F. México, Mexico 
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     title = {Controllability of linear and semilinear non-diagonalizable parabolic systems},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {1178--1204},
     publisher = {EDP-Sciences},
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     url = {http://geodesic.mathdoc.fr/articles/10.1051/cocv/2014063/}
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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

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