Lissy P, Zuazua E (2018)
Publication Type: Journal article
Publication year: 2018
Book Volume: 39
Pages Range: 281-296
Journal Issue: 2
DOI: 10.1007/s11401-018-1064-6
This paper deals 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—the authors 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. The general result is illustrated by two simple examples.
APA:
Lissy, P., & Zuazua, E. (2018). Internal Controllability for Parabolic Systems Involving Analytic Non-local Terms. Chinese Annals of Mathematics Series B, 39(2), 281-296. https://dx.doi.org/10.1007/s11401-018-1064-6
MLA:
Lissy, Pierre, and Enrique Zuazua. "Internal Controllability for Parabolic Systems Involving Analytic Non-local Terms." Chinese Annals of Mathematics Series B 39.2 (2018): 281-296.
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