Mathematical topics in collisional kinetic models

1 月 5 日上午10:30-12:00 Mathematical topics in collisional kinetic models: PART I

1 月 6 日上午10:30-12:00 Mathematical topics in collisional kinetic models: PART II

Abstract: The lectures provide an introduction to collisional kinetic equations at the mesoscopic scale, notably the Boltzmann and Landau models. We will discuss their microscopic origins and formal links to macroscopic fluid dynamics through scaling limits and, along the way, review the basic structures of these equations. A theme will be Lyapunov functionals, including entropy and Fisher information, and the dissipation identities they generate, which yield a priori estimates and insight into the behaviour of solutions.