Minimal time of controllability of two parabolic equations with disjoint control and coupling domains

摘要

We consider two parabolic equations coupled by a matrix A(x) = q(x)A_0, where A_0 is a Jordan block of order 1, and controlled by a single localized function, or by a single boundary control. The support of the coupling coefficient, q, and the control domain may be disjoint. We exhibit an explicit minimal time of null-controllability, T_0(q)∈[0,+∞].