The dampening role of large repulsive convection in a chemotaxis system modeling tumor angiogenesis. (July 2021)

• Record Type: Journal Article
• Authors: Tao, Youshan; Winkler, Michael
• Is Part Of: Nonlinear analysis. Volume 208(2021)
• Publication Date: 2021-07
• Subjects: 35A01 -- 35K57 -- 35Q92 -- 92C17; Chemotaxis -- Attraction -- Repulsion -- Angiogenesis; 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.2021.112324
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: This paper is concerned with a parabolic–parabolic–elliptic system arising as a simplified model for the initial phase of tumor-related angiogenesis. As essential characteristics, this system contains a cascade-like coupling of two chemotaxis processes involving signal production as in classical Keller–Segel systems, linked to a further repulsive cross-diffusive mechanism. It is shown that in n -dimensional bounded convex domains with n ≤ 3 and for any given suitably regular initial data, a suitable assumption on largeness of the parameter corresponding to the latter repulsion term ensures global existence of a bounded classical solution, and hence rules out the possibility of finite-time explosions which in the absence of any such chemorepulsion are known to occur at least in a certain borderline case.