Controllability of a 2 × 2 parabolic system by one force with space-dependent coupling term of order one

M Duprez (1)

1 LMB - Laboratoire de Mathématiques de Besançon (UMR 6623)

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.

Domaines: Equations aux dérivées partielles [math.AP]; Optimisation et contrôle [math.OC]; Analyse numérique [math.NA]

M Duprez. Controllability of a 2 × 2 parabolic system by one force with space-dependent coupling term of order one. 2015. ⟨hal-01174812v1⟩