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| Internal Controllability for Parabolic Systems Involving Analytic Non-local Terms |
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Citation： |
Pierre LISSY,Enrique ZUAZUA.Internal Controllability for Parabolic Systems Involving Analytic Non-local Terms[J].Chinese Annals of Mathematics B,2018,39(2):281~296 |
| Page view： 1231
Net amount： 785 |
Authors： |
Pierre LISSY; Enrique ZUAZUA |
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| 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. |
Keywords： |
Parabolic systems, Non-local potentials, Analyticity, Nullcontrollability, Kalman rank condition, Spectral unique continuation |
Classification： |
35K40, 93B05, 93B07 |
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