Global entropy solutions to a degenerate parabolic-parabolic chemotaxis system for flux-limited dispersal

Existence of global finite-time bounded entropy solutions to a parabolic-parabolic system proposed in [16] is established in bounded domains under no-flux boundary conditions for nonnegative bounded initial data. This modification of the classical Keller-Segel model features degenerate diffusion and chemotaxis that are both subject to flux-saturation. The approach is based on Schauder’s fixed point theorem and calculus of functions of bounded variation.