Geodesic
Controllability of a 2×2 parabolic system by one force with space-dependent coupling term of order one
Duprez, Michel1 
1 Laboratoire de Mathématiques de Besançon UMR CNRS 6623, Université de Franche-Comté, 16 route de Gray, 25030 Besançon cedex, France.
ESAIM: Control, Optimisation and Calculus of Variations, Tome 23 (2017) no. 4, pp. 1473-1498 Cet article a éte moissonné depuis la source Numdam

Voir la notice de l'article

This paper is devoted to the controllability of linear systems of two coupled parabolic equations when the coupling involves a space dependent first order term. This system is set on an bounded interval I⊂⊂R, and the first equation is controlled by a force supported in a subinterval of I or on the boundary. In the case where the intersection of the coupling and control domains is nonempty, we prove null controllability at any time. Otherwise, we provide a minimal time for null controllability. Finally we give a necessary and sufficient condition for the approximate controllability. The main technical tool for obtaining these results is the moment method.

DOI : 10.1051/cocv/2016061
Classification : 93B05, 93B07
Keywords: Controllability, observability, moment method, parabolic systems

Duprez, Michel 1

1 Laboratoire de Mathématiques de Besançon UMR CNRS 6623, Université de Franche-Comté, 16 route de Gray, 25030 Besançon cedex, France. 
@article{COCV_2017__23_4_1473_0,
     author = {Duprez, Michel},
     title = {Controllability of a $2 \times{} 2$ parabolic system by one force with space-dependent coupling term of order one},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {1473--1498},
     year = {2017},
     publisher = {EDP-Sciences},
     volume = {23},
     number = {4},
     doi = {10.1051/cocv/2016061},
     mrnumber = {3716929},
     zbl = {1375.93018},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/cocv/2016061/}
}
TY  - JOUR
AU  - Duprez, Michel
TI  - Controllability of a $2 \times{} 2$ parabolic system by one force with space-dependent coupling term of order one
JO  - ESAIM: Control, Optimisation and Calculus of Variations
PY  - 2017
SP  - 1473
EP  - 1498
VL  - 23
IS  - 4
PB  - EDP-Sciences
UR  - http://geodesic.mathdoc.fr/articles/10.1051/cocv/2016061/
DO  - 10.1051/cocv/2016061
LA  - en
ID  - COCV_2017__23_4_1473_0
ER  - 
%0 Journal Article
%A Duprez, Michel
%T Controllability of a $2 \times{} 2$ parabolic system by one force with space-dependent coupling term of order one
%J ESAIM: Control, Optimisation and Calculus of Variations
%D 2017
%P 1473-1498
%V 23
%N 4
%I EDP-Sciences
%U http://geodesic.mathdoc.fr/articles/10.1051/cocv/2016061/
%R 10.1051/cocv/2016061
%G en
%F COCV_2017__23_4_1473_0
Duprez, Michel. Controllability of a $2 \times{} 2$ parabolic system by one force with space-dependent coupling term of order one. ESAIM: Control, Optimisation and Calculus of Variations, Tome 23 (2017) no. 4, pp. 1473-1498. doi: 10.1051/cocv/2016061

Cité par Sources :