Internal controllability for parabolic systems involving analytic non-local terms
Lissy, Pierre; Zuazua, Enrique (2018), Internal controllability for parabolic systems involving analytic non-local terms, Chinese Annals of Mathematics. Series B, 39, 2, p. 281-296. 10.1007/s11401-018-1064-6
TypeArticle accepté pour publication ou publié
External document linkhttps://hal.archives-ouvertes.fr/hal-01574999
Journal nameChinese Annals of Mathematics. Series B
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Abstract (EN)We deal with the problem of internal controllability of a system of heat equations posed on a bounded domain with Dirichlet boundary conditions and perturbed with analytic non-local coupling terms. Each component of the system may be controlled in a different subdomain. Assuming that the unperturbed system is controllable-a property that has been recently characterized in terms of a Kalman-like rank condition-, we give a necessary and sufficient condition for the controllability of the coupled system under the form of a unique continuation property for the corresponding elliptic eigenvalue system. The proof relies on a compactness-uniqueness argument, which is quite unusual in the context of parabolic systems, previously developed for scalar parabolic equations. Our general result is illustrated by two simple examples.
Subjects / Keywordsparabolic systems; non-local potentials; null controllability; Kalman rank condition; spectral unique continuation
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