Incompressible limit of a continuum model of tissue growth for two cell populations

Pierre Degond; Sophie Hecht; Nicolas Vauchelet; Pierre Degond; Sophie Hecht; Nicolas Vauchelet

doi:10.3934/nhm.2020003

Networks and Heterogeneous Media

2020, Volume 15, Issue 1: 57-85. doi: 10.3934/nhm.2020003

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Incompressible limit of a continuum model of tissue growth for two cell populations

1.
Department of Mathematics, Imperial College London, London SW7 2AZ, UK
2.
Francis Crick Institute, 1 Midland Rd, London NW1 1AT, UK
3.
LAGA, Universite Paris 13, 99 avenue Jean-Baptiste Clement, 93430 Villetaneuse, France

Received: 01 January 2019 Revised: 01 September 2019
Primary: 35K55; 35R35; Secondary: 65M08; 92C15; 92C10

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.
- Tissue growth,
- Two cell populations,
- Incompressible limit,
- Free boundary problem
Citation: Pierre Degond, Sophie Hecht, Nicolas Vauchelet. Incompressible limit of a continuum model of tissue growth for two cell populations[J]. Networks and Heterogeneous Media, 2020, 15(1): 57-85. doi: 10.3934/nhm.2020003

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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.

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