On a non-isothermal Cahn-Hilliard model for tumor growth

TL;DR

This paper introduces a thermodynamically consistent non-isothermal Cahn-Hilliard model for tumor growth that accounts for temperature changes, nutrient dynamics, cell proliferation, and apoptosis, with a focus on proving the existence of weak entropy solutions.

Contribution

The paper presents a novel non-isothermal Cahn-Hilliard model for tumor growth incorporating thermodynamic consistency and proves the existence of weak entropy solutions.

Findings

Model successfully describes tumor growth with temperature effects

Existence of weak entropy solutions established

Captures nutrient consumption and cell proliferation dynamics

Abstract

We introduce here a new diffuse interface thermodynamically consistent non-isothermal model for tumor growth in presence of a nutrient in a domain $\Omega \subset \mathbb{R}^3$. In particular our system describes the growth of a tumor surrounded by healthy tissues, taking into account changes of temperature, proliferation of cells, nutrient consumption and apoptosis. Our aim consists in proving an existence result for weak entropy solutions to our model.