Date: Fri. February 11, 2022
Organized by: Durham University, Seminars in Mathematical Sciences
Title: Explicit decay rates for discrete velocity BGK models
Abstract. In this talk we analyse the long-time behaviour of solutions to prototypical transport-relaxation systems of BGK-type. We present a hypocoercivity method that modifies the standard norm based on Lyapunov matrix inequalities. The method provides optimal decay rates for constant relaxation rates, where the equation can be Fourier decomposed into finite ODEs. Expressing the Lyapunov functional through pseudo-differential operators allows us to go beyond the ODE approach and prove explicit decay rates for spatially non-homogeneous relaxation. We further discuss how the two-velocity example connects the presented method to other hypocoercivity methods. This is joint work with Anton Arnold, Amit Einav and Beatrice Signorello.