A kinetic chemotaxis model and its diffusion limit in slab geometry

Chemotaxis describes the intricate interplay of cellular motion in response to a chemical signal. We here consider the case of slab geometry which models chemotactic motion between two infinite membranes. Like previous works, we are particularly interested in the asymptotic regime of high tumbling rates. We establish local existence and uniqueness of solutions to the kinetic equation and show their convergence towards solutions of a parabolic Keller-Segel model in the asymptotic limit. In addition, we prove convergence rates with respect to the asymptotic parameter under additional regularity assumptions on the problem data. Particular difficulties in our analysis are caused by vanishing velocities in the kinetic model as well as the occurrence of boundary terms.