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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Contributeur : Michel Duprez <>
Soumis le : mardi 9 août 2016 - 10:05:36
Dernière modification le : mercredi 10 août 2016 - 01:04:02

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  • HAL Id : hal-01174812, version 2

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M Duprez. Controllability of a 2 × 2 parabolic system by one force with space-dependent coupling term of order one. 2016. 〈hal-01174812v2〉

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