| Issue |
ESAIM: COCV
Volume 21, Number 4, October-December 2015
|
|
|---|---|---|
| Page(s) | 1178 - 1204 | |
| DOI | https://doi.org/10.1051/cocv/2014063 | |
| Published online | 06 July 2015 | |
Controllability of linear and semilinear non-diagonalizable parabolic systems∗
1
Dpto, E.D.A.N., Universidad de Sevilla,
Aptdo. 1160, 41080
Sevilla,
Spain
cara@us.es & manoloburgos@us.es
2
Instituto de Matemáticas, Universidad Nacional Autónoma de
México, Circuito Exterior,
C.U.
04510
D.F. México,
Mexico
ldeteresa@im.unam.mx
Received:
15
March
2012
Revised:
29
April
2014
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.
Mathematics Subject Classification: 93B05 / 35K20
Key words: Null controllability / parabolic / non-diagonalizable
© EDP Sciences, SMAI, 2015
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