Seminar Analysis and Mathematical Physics: Dr. Havva Yoldas (University of Vienna)

Obtaining quantitative hypocoercivity estimates by using Harris-type theorems.

 I will talk about Harris-type theorems and their applications to several kinetic equations like the linear BGK, the linear Boltzmann, the kinetic Fokker-Planck equations and some biological kinetic models like the run and tumble equation. Even though the original ideas date back to the 1940s, the Harris-type arguments recently raised a lot of mathematical interest in the PDE community especially after a simplified proof provided by Hairer and Mattingly in 2011. It is a convenient way to obtain quantifiable convergence rates, constructive proofs and the existence of a unique stationary state comes as a by-product of the theorems. The latter is especially useful for kinetic equations arising in biology where the shape of the stationary state cannot be known a priori. 

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