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

2024/01/08 by Zhigun, Anna
#26B30 35K55 35K65 35M30 35Q92 92C17 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2401.03887

Abstract

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.

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