  This paper is devoted to the controllability of linear systems of two coupled
parabolic equations when the coupling involves a space dependent first order
term. This system is set on an bounded interval, and the first equation is
controlled by a force supported in a subinterval of I or on the boundary. In
the case where the intersection of the coupling and control domains is
nonempty, we prove null controllability at any time. Otherwise, we provide a
minimal time for null controllability. Finally we give a necessary and
sufficient condition for the approximate controllability. The main technical
tool for obtaining these results is the moment method
