Existence of weak solutions to the Keller–Segel chemotaxis system with additional cross-diffusion. (August 2020)

• Record Type: Journal Article
• Authors: Arumugam, Gurusamy; Erhardt, André H.; Eswaramoorthy, Indurekha; Krishnan, Balachandran
• Is Part Of: Nonlinear analysis. Volume 54(2020)
• Publication Date: 2020-08
• Subjects: Keller–Segel system -- Weak solutions -- Fixed point theorem; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2020.103090
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: In this paper, we consider the Keller–Segel chemotaxis system with additional cross-diffusion term in the second equation. This system is consisting of a fully nonlinear reaction–diffusion equations with additional cross-diffusion. We establish the existence of weak solutions to the considered system by using Schauder's fixed point theorem, a priori energy estimates and the compactness results.