CERAMATHS - DMATHS seminar: presentation by Romain Loyer

The wave equation with variable coefficients models the propagation of physical quantities (such as waves, temperature, distortion, concentration, etc.) in a heterogeneous medium. The coefficients take into account conductivity, dissipation, density, reactions, velocity and other factors acting on the system.

In this talk, we discuss the controllability of such an equation. To do so, we use the backstepping method on the first-order system associated with the wave equation. We then obtain a control and a finite-time stabilizable solution to the problem.
In addition, this method gives us a direct method for the controllability of the system (i.e. not based on observability). This gives us an effective method for numerically approximating the control and solution of waves. Some simulation results will be presented to demonstrate stabilization.