Global dynamics in a chemotaxis model describing tumor angiogenesis with/without mitosis in any dimensions

TL;DR

This paper investigates a chemotaxis model for tumor angiogenesis across any dimensions, establishing conditions for global boundedness and stability, and showing that certain factors do not lead to pattern formation.

Contribution

It provides new sufficient conditions for global boundedness and stability in a chemotaxis model in arbitrary dimensions, extending previous lower-dimensional results.

Findings

Identified three simple conditions for global boundedness.

Established two types of global stability for solutions.

Showed that absence of chemotaxis and ECs mitosis prevent pattern formation.

Abstract

In this work, we study the Neumann initial boundary value problem for a three-component chemotaxis model in any dimensional bounded and smooth domains; this model is used to describe the branching of capillary sprouts during angiogenesis. First, we find three qualitatively simple sufficient conditions for qualitative global boundedness, and then, we establish two types of global stability for bounded solutions in qualitative ways. As a consequence of our findings, the underlying system without chemotaxis and the effect of ECs mitosis can not give rise to pattern formations. Our findings quantify and extend significantly previous studies, which are set in lower dimensional convex domains and are with no qualitative information.