[INS Distinguished Lecture] Control Theory meets Kinetic Theory

We will start by a brief introduction to the so-called control theory in analysis of partial differential equations. This theory was initially developed for hyperbolic and parabolic problems (such as propagation of waves and diffusion of heat). However, many fundamental physical equations combine a transport hyperbolic term with a partially dissipative one: kinetic theory in particular presents such structure. We will then discuss a recent work (with F. Hérau, H. Hutridurga and H. Dietert) where we study a class of such equations for which the dissipation on the kinetic variable is active only on part of the spatial domain. We prove quantitative estimates of exponential stabilization under a geometric control condition reminiscent of control theory of wave equations. The proof relies on a new approach to hypocoercivity based on trajectories and quantitative divergence inequalities.

Bio:
Clément Mouhot is Professor of Mathematical Sciences in the Department of Pure Mathematics and Mathematical Statistics at the University of Cambridge. He was a CNRS researcher at ÉNS Paris before joining Cambridge in 2010. His research is primarily in analysis and mathematical physics. He obtained his PhD in 2004 under the supervision of Cedric Villani at the ÉNS Lyon. He was awarded the Whitehead Prize by the LMS, a “Grand Prix” by the French academy of science, and the Adams Prize by the University of Cambridge, and was an invited section speaker at the ICM in 2018.