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

Duprez, Michel; Lissy, Pierre (2018), Positive and negative results on the internal controllability of parabolic equations coupled by zero and first order terms, Journal of Evolution Equations, 18, 2, p. 659-680. 10.1007/s00028-017-0415-1

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Article accepté pour publication ou publié
External document link
https://hal.archives-ouvertes.fr/hal-01370955
Date
2018
Journal name
Journal of Evolution Equations
Volume
18
Number
2
Publisher
Springer
Pages
659-680
Publication identifier
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Author(s)
Duprez, Michel cc
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Lissy, Pierre
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Abstract (EN)
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.
Subjects / Keywords
Controllability; Parabolic systems; Fictitious control method; Algebraic solvability