# Minimal time of controllability for some parabolic systems

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

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.

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