# Uniform convergence for the incompressible limit of a tumor growth model

## TL;DR

This paper proves uniform convergence of tumor density and pressure in a model based on Brinkman's Law as it approaches the incompressible limit, using viscosity solutions to handle the lack of maximum principle.

## Contribution

It introduces a novel approach to establish uniform convergence in a tumor growth model governed by Brinkman's Law, overcoming the challenge of missing maximum principle.

## Key findings

- Established optimal uniform convergence of tumor density and pressure
- Extended viscosity solution methods to a non-standard tumor growth system
- Addressed the absence of maximum principle in the analysis

## Abstract

We study a model introduced by Perthame and Vauchelet that describes the growth of a tumor governed by Brinkman's Law, which takes into account friction between the tumor cells. We adopt the viscosity solution approach to establish an optimal uniform convergence result of the tumor density as well as the pressure in the incompressible limit. The system lacks standard maximum principle, and thus modification of the usual approach is necessary.