  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.
