On a nonlinear model for tumor growth in a cellular medium

TL;DR

This paper develops and analyzes a nonlinear continuum model for tumor growth in a cellular medium, accounting for variable cell density and multiphase flow, and establishes the existence of global weak solutions.

Contribution

It introduces a novel nonlinear tumor growth model with variable density and proves the existence of global weak solutions using advanced mathematical techniques.

Findings

Existence of global-in-time weak solutions.

Model captures variable cell density in tumor growth.

Mathematical framework based on penalization and compactness arguments.

Abstract

We investigate the dynamics of a nonlinear model for tumor growth within a cellular medium. In this setting the "tumor" is viewed as a multiphase flow consisting of cancerous cells in either proliferating phase or quiescent phase and a collection of cells accounting for the "waste" and/or dead cells in the presence of a nutrient. Here, the tumor is thought of as a growing continuum $\Omega$ with boundary $\partial \Omega$ both of which evolve in time. The key characteristic of the present model is that the total density of cancerous cells is allowed to vary, which is often the case within cellular media. We refer the reader to the articles \cite{Enault-2010}, \cite{LiLowengrub-2013} where compressible type tumor growth models are investigated. Global-in-time weak solutions are obtained using an approach based on penalization of the boundary behavior, diffusion, viscosity and pressure in the weak formulation, as well as convergence and compactness arguments in the spirit of Lions \cite{Lions-1998} (see also \cite{Feireisl-book, DT-MixedModel-2013}).