Controllability of a 2 × 2 parabolic system by one force with space-dependent coupling term of order one - Archive ouverte HAL Access content directly
Journal Articles ESAIM: Control, Optimisation and Calculus of Variations Year : 2017

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

Abstract

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.
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Dates and versions

hal-01174812 , version 1 (09-07-2015)
hal-01174812 , version 2 (09-08-2016)

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M Duprez. Controllability of a 2 × 2 parabolic system by one force with space-dependent coupling term of order one. ESAIM: Control, Optimisation and Calculus of Variations, 2017, 23, p. 1473-1498. ⟨10.1051/cocv/2016061⟩. ⟨hal-01174812v2⟩
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