Weak solutions to triangular cross diffusion systems modeling chemotaxis with local sensing. (January 2023)

• Record Type: Journal Article
• Authors: Desvillettes, Laurent; Laurençot, Philippe; Trescases, Ariane; Winkler, Michael
• Is Part Of: Nonlinear analysis. Volume 226(2023)
• Publication Date: 2023-01
• Subjects: Global existence -- Weak solutions -- Comparison -- Stabilization -- Chemotaxis; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2022.113153
• Languages: English
• ISSNs: 0362-546X

Abstract

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.