Positive and negative results on the internal controllability of parabolic equations coupled by zero and first order terms

Michel Duprez 1 Pierre Lissy 2
2 CEREMADE, Universit e Paris Dauphine
CEREMADE - CEntre de REcherches en MAthématiques de la DEcision
Abstract : This paper is devoted to studying the null and approximate controllability of two linear coupled parabolic equations posed on a smooth domain Ω of R^N with coupling terms of zero and first orders and one control localized in some arbitrary nonempty open subset ω of the domain Ω. We prove the null controllability under a new sufficient condition and we also provide the first example of a not approximately controllable system in the case where the support of one of the nontrivial first order coupling terms intersects the control domain ω.
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Journal of Evolution Equations, Springer Verlag, A Paraître, 〈10.1007/s00028-017-0415-1〉
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Michel Duprez, Pierre Lissy. Positive and negative results on the internal controllability of parabolic equations coupled by zero and first order terms. Journal of Evolution Equations, Springer Verlag, A Paraître, 〈10.1007/s00028-017-0415-1〉. 〈hal-01370955〉

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