Approximate and null controllability of a parabolic system with coupling terms of order one

We study two notions of controllability on a parabolic system with coupling terms of order one. Based on existing results on, on one side parabolic systems with coupling terms of order zero, and on the other one parabolic systems with coupling terms of order one where the control domain is an interval, we give here some controllability conditions in the case where the coupling term is of order one and the control domain is not necessarily an interval.