Long-time behavior of an angiogenesis model with flux at the tumor boundary

TL;DR

This paper analyzes a nonlinear PDE model of tumor-induced angiogenesis with flux at the tumor boundary, demonstrating how key parameters determine whether solutions stabilize to different stationary states over time.

Contribution

It provides a mathematical analysis of the long-term behavior of an angiogenesis model incorporating nonlinear flux and chemotaxis, highlighting parameter influence on system stability.

Findings

Solutions converge to semi-trivial stationary states depending on parameters

Parameter ranges dictate long-time behavior and stability

Model captures key dynamics of tumor-induced angiogenesis

Abstract

This paper deals with a nonlinear system of partial differential equations modeling a simplified tumor-induced angiogenesis taking into account only the interplay between tumor angiogenic factors and endothelial cells. Considered model assumes a nonlinear flux at the tumor boundary and a nonlinear chemotactic response. It is proved that the choice of some key parameters influences the long-time behaviour of the system. More precisely, we show the convergence of solutions to different semi-trivial stationary states for different range of parameters.