We consider a one-dimensional 2 × 2 parabolic equations, simultaneously controllable by a localized function in their source term. We also consider a simultaneous boundary control. In each case, we prove the existence of minimal time T0(q) of null controllability, that is to say, the corresponding problem is null controllable at any time T > T0(q) and not null controllable for T < T0(q). We also prove that one can expect any minimal time associated to the boundary control problem.
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