Asymptotic behaviour of global solutions to a model of cell invasion

TL;DR

This paper investigates the long-term behavior of solutions to a mathematical model describing cell invasion, establishing conditions for global existence and analyzing how solutions behave asymptotically over time.

Contribution

It provides a rigorous analysis of the global well-posedness and asymptotic behavior of solutions to a coupled PDE system modeling cell invasion, which was not previously characterized.

Findings

Proved global existence of solutions under certain conditions

Characterized the asymptotic behavior of solutions as time approaches infinity

Identified key factors influencing the invasion process dynamics

Abstract

In this paper we analyze a mathematical model focusing on key events of the cells invasion process. Global well-possedness and asymptotic behaviour of nonnegative solutions to the corresponding coupled system of three nonlinear partial differential equations are studied.