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. In the slab geometry, the motion takes place between two infinite membranes. Like in previous investigations, the asymptotic regime of high tumbling rates is of particular interest. This work provides local existence and uniqueness of solutions to the kinetic equation and shows their convergence towards solutions of a parabolic Keller–Segel model in the asymptotic limit. In addition, convergence rates with respect to the asymptotic parameter are established under additional regularity assumptions on the problem data. Particular difficulties in the analysis are caused by vanishing velocities in the kinetic model as well as the occurrence of boundary terms.