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

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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. 
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     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},
     publisher = {EDP-Sciences},
     volume = {23},
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     year = {2017},
     doi = {10.1051/cocv/2016061},
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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

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