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

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.