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

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

Indirect controllability of locally coupled systems under geometric conditions

First author supported by the Fondation des Sciences Mathématiques de Paris. Both authors partially GDRE CONEDP (CNRS/INDAM/UP)International audienceWe consider systems of two wave/heat/Schrödinger-type equations coupled by a zero order term, only one of them being controlled. We prove an internal and a boundary null-controllability result in any space dimension, provided that both the coupling and the control regions satisfy the Geometric Control Condition. This includes several examples in which these two regions have an empty intersection

Reachability problems for a wave-wave system with a memory term

We solve the reachability problem for a coupled wave-wave system with an integro-differential term. The control functions act on one side of the boundary. The estimates on the time is given in terms of the parameters of the problem and they are explicitly computed thanks to Ingham type results. Nevertheless some restrictions appear in our main results. The Hilbert Uniqueness Method is briefly recalled. Our findings can be applied to concrete examples in viscoelasticity theor

Indirect controllability of locally coupled wave-type systems and applications

We consider symmetric systems of two wave-type equations only one of them being controlled. The two equations are coupled by zero order terms, localized in part of the domain. We prove an internal and a boundary null-controllability result in any space dimension, provided that both the coupling and the control regions satisfy the Geometric Control Condition. We deduce similar null-controllability results in any positive time for parabolic systems and Schrödinger-type systems under the same geometric conditions on the coupling and the control regions. This includes several examples in which these two regions have an empty intersection