GLOBAL WELL-POSEDNESS OF THE KDV EQUATION ON A STAR-SHAPED NETWORK AND STABILIZATION BY SATURATED CONTROLLERS

摘要

In this work, we deal with the global well-posedness and stability of the linear and nonlinear Korteweg-de Vries equations on a finite star-shaped network by acting with saturated controls. We obtain the global well-posedness by using the Kato smoothing property for the linear case and then using some estimates and a fixed point argument we deal with the nonlinear system. Finally, we obtain the exponential stability using two different kinds of saturation by proving an observability inequality via a contradiction argument.