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This paper is devoted to the controllability of linear systems of two coupledparabolic equations when the coupling involves a space dependent first orderterm. This system is set on an bounded interval, and the first equation iscontrolled by a force supported in a subinterval of I or on the boundary. Inthe case where the intersection of the coupling and control domains isnonempty, we prove null controllability at any time. Otherwise, we provide aminimal time for null controllability. Finally we give a necessary andsufficient condition for the approximate controllability. The main technicaltool for obtaining these results is the moment method

Controllability of a 2x2 parabolic system by one force with a space-dependent coupling term of order one