  This work addresses controllability properties for some systems of partial
differential equations in which the main feature is the coupling through
nonlocal integral terms. In the first part, we study a nonlinear
parabolic-elliptic system arising in mathematical biology and, using recently
developed techniques, we show how Carleman estimates can be directly used to
handle the nonlocal terms, allowing us to implement well-known strategies for
controlling coupled systems and nonlinear problems. In the second part, we
investigate fine controllability properties of a 1-d linear nonlocal
parabolic-parabolic system. In this case, we will see that the controllability
of the model can fail and it will depend on particular choices and combinations
of local and nonlocal couplings.
