The dampening role of large repulsive convection in a chemotaxis system modeling tumor angiogenesis

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.