New phenomena for the null controllability of parabolic systems: Minimal time and geometrical dependence

We consider the null controllability problem for two coupled parabolic equations with a space-depending coupling term. We analyze both boundary and distributed null controllability. In each case, we exhibit a minimal time of control, that is to say, a time T0∈[0,∞]T0∈[0,∞] such that the corresponding system is null controllable at any time T>T0T>T0 and is not if T