Seminário Luiz Adauto Medeiros de Análise/EDP - 29/11/2022

Palestrante: Ludovick Gagnon (Université de Lorraine, CNRS, Inria équipe SPHINX)

Resumo: The backstepping method has become a popular way to design feedback laws for the rapid stabilization of a large class of PDEs. This method essentially reduces the proof of exponential stability to the existence and invertibility of a transformation. Initially applied with a Volterra transformation, the Fredholm alternative, introduced by Coron and Lü, allows to overcome some existence issues for the Volterra transformation. This new approach also has the advantage of having a systematic methodology, but the methods known until now were only applicable to differential operators D_x^a with a>3/2. In this talk, we present the duality/compactness method to surmount this threshold and show that the Fredholm-type backstepping method applies for anti-adjoint operators i |D_x|^a, with a >1. We will demonstrate the application of this result for the rapid stabilization of the linearized water waves equation.