23/03/2021 – 14h00-15h00 – Online
Control and Feedback stabilization for entropy solutions to conservation laws
Abstract. Hyperbolic conservation laws are partial differential equations that are used to model many kind of physical phenomena: gas dynamics, traffic flow, electromagnetism, shallow water theory, combustion theory…
However even the simplest equation of this kind, the so called Burgers’ equation can be shown to blow up generically. In the ’60s, people developed the concept of entropy solutions to regain global existence and uniqueness of solutions, but for such solutions the « linearization paradigm » can be shown to fail: the nonlinear problem has local properties that are very different than the linearized system. This is particularly striking in the context of control theory as we will explain. This also leads to the failure of most the methods used for other nonlinear PDEs to get exact controllability and feedback stabilization.
In this talk, after providing some background on entropy solutions, we will describe some of the few results and techniques that are available for this kind of equations in this context of solutions.
Biography. Vincent Perrollaz is assistant professor at Institut Denis Poisson in Université de Tours. He received his PhD in 2011 at Laboratoire Jacques-Louis Lions, then Université Pierre et Marie Curie. He mostly works on partial differential equations of hyperbolic type and control theory.
Practical details. The seminar will take place online, using Microsoft Teams. If you want to attend this seminar (or any of the forthcoming online Automatiques seminars), and if you do not already have access to the AutoSeminar group on Teams, simply send an email and you will be invited. Please specify which email address the invitation must be sent to (this has to be the address associated with your Teams account). You will find the link to the seminar on the « General » AutoSeminar channel on Teams, approximately 15 minutes before the beginning.
The technical side of things: you can use Teams either directly from you web browser or using the « fat client », which is available for most platforms (Windows, Linux, Mac, Android & iOS). We strongly recommend the latter option whenever possible. Please give it a try before the seminar to anticipate potential problems.