Deriving diffusion equations from nonlinear kinetic equations

Vortrag von Havva Yoldaş

Datum: 25.09.25  Zeit: 16.00 - 17.00  Raum: ETH HG G 19.2

We will derive a class of nonlinear diffusion equations (covering both porous media and fast diffusion equations) as the hydrodynamic limit of a class of nonlinear, spatially inhomogeneous kinetic equations of BGK-type. These equations share the same superlinearity as the Boltzmann equation and fall into the class of run and tumble equations appearing in mathematical biology. We will look at the Cauchy problem under the parabolic scaling and also provide a quantitative nonlinear hypocoercivity result. The derivation is based on both the hypocoercivity and relative entropy methods. The talk is based on a joint work with Daniel Morris (TU Delft) and Josephine Evans (University of Warwick).