---
abstract: 'This paper investigates the incompressible limit of a system modelling the growth of two cells population. The model describes the dynamics of cell densities, driven by pressure exclusion and cell proliferation. It has been shown that solutions to this system of partial differential equations have the segregation property, meaning that two population initially segregated remain segregated. This work is devoted to the incompressible limit of such system towards a free boundary Hele Shaw type model for two cell populations.'
author:
- Pierre Degond
- Sophie Hecht
- Nicolas Vauchelet
bibliography:
- 'Cell\_sorting\_segregation\_v12\_2.bib'
title: Incompressible limit of a continuum model of tissue growth for two cell populations
---

[**[Acknowledgements. ]{}** PD acknowledges support by the Engineering and Physical Sciences Research Council (EPSRC) under grants no. EP/M006883/1, EP/N014529/1 and EP/P013651/1, by the Royal Society and the Wolfson Foundation through a Royal Society Wolfson Research Merit Award no. WM130048 and by the National Science Foundation (NSF) under grant no. RNMS11-07444 (KI-Net). PD is on leave from CNRS, Institut de Mathématiques de Toulouse, France. SH acknowledge support from the Francis Crick Institute which receives its core funding from Cancer Re- search UK (FC001204), the UK Medical Research Council (FC001204), and the Well- 