Weak solutions to triangular cross diffusion systems modeling chemotaxis with local sensing

TL;DR

This paper establishes new mathematical estimates and proves global existence for a class of chemotaxis models with cross diffusion, demonstrating convergence to steady states under certain conditions.

Contribution

It introduces novel estimates and global existence results for chemotaxis systems with local sensing, including convergence analysis using Lyapunov functionals.

Findings

Global existence of solutions is proven.

Convergence to homogeneous steady states is shown for sublinear motility functions.

A Lyapunov functional is constructed for stability analysis.

Abstract

New estimates and global existence results are provided for a class of systems of cross diffusion equations arising from the modeling of chemotaxis with local sensing, possibly featuring a growth term of logistic-type as well. For sublinear non-increasing motility functions, convergence to the spatially homogeneous steady state is shown, a dedicated Lyapunov functional being constructed for that purpose.