Minimal time of controllability for some parabolic systems

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Date/heure
Date(s) - 18/03/2014
10 h 00 min - 11 h 00 min

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In this talk we will study the controllability properties of two kind of coupled parabolic systems. In the first problem, the control is exerted in a part \omega of the domain (distributed control) and in the second one, on a part of the boundary of the domain (boundary control). In both cases we will see that, even if the problem under consideration is parabolic, an explicit minimal time of controllability $T_0 \in [0, \infty] $ arises. Thus, the corresponding system is not null controllable at time $T$ if $T< T_0$ and it is null controllable at time $T$ when $T>T_0$. This minimal time is related to: The action and the geometric position of the support of the coupling term when this support does not intersect the control domain $\omega$ in the case of the distributed control or the condensation index of the complex sequence of eigenvalues of the corresponding matrix elliptic operator in the case of the boundary control.

Olivier CHABROL
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