Analysis of a Cahn-Hilliard-Brinkman model for tumour growth with chemotaxis

TL;DR

This paper introduces and analyzes a new Cahn-Hilliard-Brinkman model for tumor growth that incorporates chemotaxis and uses outflow boundary conditions, proving the existence of global weak solutions.

Contribution

It presents a novel mathematical model combining Cahn-Hilliard, Brinkman flow, and chemotaxis for tumor growth, with rigorous existence analysis.

Findings

Existence of global-in-time weak solutions proven.

Model accommodates chemotaxis and realistic boundary conditions.

Provides a mathematical foundation for future tumor growth simulations.

Abstract

Phase field models recently gained a lot of interest in the context of tumour growth models. Typically Darcy-type flow models are coupled to Cahn-Hilliard equations. However, often Stokes or Brinkman flows are more appropriate flow models. We introduce and mathematically analyse a new Cahn-Hilliard-Brinkman model for tumour growth allowing for chemotaxis. Outflow boundary conditions are considered in order not to influence tumour growth by artificial boundary conditions. Existence of global-in-time weak solutions is shown in a very general setting.