Internal Controllability for Parabolic Systems Involving Analytic Non-local Terms

Lissy P, Zuazua E (2018)

Publication Type: Journal article

Publication year: 2018

Journal

Chinese Annals of Mathematics Series B World Scientific Publishing / Springer Verlag (Germany)

Book Volume: 39

Pages Range: 281-296

Journal Issue: 2

DOI: 10.1007/s11401-018-1064-6

Abstract

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.

Authors with CRIS profile

Enrique Zuazua Iriondo

Involved external institutions

University of Paris 9 - Paris-Dauphine / Université Paris 9 Paris-Dauphine FR France (FR) University of Deusto / Universidad de Deusto ES Spain (ES)

How to cite

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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