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We prove controllability results for abstract systems of weakly coupled $N$evolution equations in cascade by a reduced number of boundary or locallydistributed controls ranging from a single up to $N-1$ controls. We giveapplications to cascade coupled systems of $N$ multi-dimensional-hyperbolic,parabolic and diffusive equations.

Controllability of cascade coupled systems of multi-dimensional evolution PDE's by a reduced number of controls