The Korteweg-de Vries (KdV) equation, was introduced as a model to describe the propagation of long water waves in a channel. This nonlinear third order dispersive equation has been many studied in the past years from different points of view, in particular its controllability and stabilization properties. In this talk, we focus on the stabilization and controllability of the KdV equation on a star shaped network. In the first part, we study the controllability problem of star network of N KdV equations. By using Carleman estimates, we show that the system is null controllable acting in N-1 edges. Then, we pass to the KdV equation posed in a star network with bounded and unbounded lengths. Here, we show the exponential stability by acting with damping terms, not necessarily in all the branches. This talk is based on joint works with E. Crépeau, C. Prieur.
Romain Duboscq, Ariane Trescases