Séminaire du CERAMATHS - DMATHS : exposé d'Amaury Hayat

Le séminaire du département de mathématiques du CERAMATHS accueillera à 14h Amaury Hayat (CERMICS, École des Ponts Paristech), pour l'exposé suivant :

Stabilization of PDE systems

We present recent advances in the stabilization of PDEs. We will first discuss the influence of adding a small viscosity to the stabilization of one-dimensional hyperbolic systems. Then, we will discuss the Fredholm backstepping method. Backstepping is a way of reformulating the stabilization problem in a different way : it consists in finding a control operator such that the PDE system can be inversely mapped to a simpler PDE system for which stability is known. Surprisingly powerful, this approach offers the possibility to treat very general classes of systems. We will review the origin of the method and present new results that we illustrate on the stabilization of the linearized water wave equations with arbitrary decay rate. We will also examine traffic flow stabilization from both a practical and PDE perspective. Finally, we will briefly discuss some results on AI for mathematics, especially in control and stabilization, with two questions : can an AI guess the solution of a mathematical problem ? Can it even prove a theorem ?