|Publication ahead of print|
|Published online||06 September 2017|
Controllability of a 2 × 2 parabolic system by one force with space-dependent coupling term of order one∗
Laboratoire de Mathématiques de Besançon UMR CNRS 6623, Université de Franche-Comté, 16 route de Gray, 25030 Besançon cedex, France.
Received: 9 July 2015
Revised: 5 March 2016
Accepted: 14 September 2016
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.
Mathematics Subject Classification: 93B05 / 93B07
Key words: Controllability / observability / moment method / parabolic systems
© EDP Sciences, SMAI 2017
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