On the long time behavior of a tumor growth model

TL;DR

This paper analyzes the long-term behavior of a tumor growth model combining Cahn-Hilliard and reaction-diffusion equations, proving the existence of a global attractor under realistic conditions.

Contribution

It establishes the existence of a global attractor for a diffuse interface tumor growth model, demonstrating its long-time stability and dynamics.

Findings

The model generates a dissipative dynamical system.

Existence of a global attractor is proved.

The results hold under physically motivated assumptions.

Abstract

We consider the problem of the long time dynamics for a diffuse interface model for tumor growth. The model describes the growth of a tumor surrounded by host tissues in the presence of a nutrient and consists in a Cahn-Hilliard-type equation for the tumor phase coupled with a reaction-diffusion equation for the nutrient concentration. We prove that, under physically motivated assumptions on parameters and data, the corresponding initial-boundary value problem generates a dissipative dynamical system that admits the global attractor in a proper phase space.