Simultaneous and indirect control of waves: Some recent developments and open problems

The control of a single wave equation has known some tremendous amount of activity since the pioneering works of Russell in the sixties and seventies, and especially after the publication of Lions' monographs on controllability. However, the control of multi-component systems of wave equations can be arguably said to be at an early stage. In these notes, I discuss some of my recent works in this area, focusing on the notion of simultaneous control (using the same control scheme in all components of the system at hand), and indirect control (using a single control for a system consisting of two components). I also discuss some problems that I deem important to investigate.