Incompressible limit of a continuum model of tissue growth for two cell populations
File(s)Cell_sorting_segregation_rev2_v4.pdf (999.42 KB)
Accepted version
Author(s)
Degond, Pierre
Hecht, Sophie
Vauchelet, Nicolas
Type
Journal Article
Abstract
This paper investigates the incompressible limit of a system modelling the growth oftwo cells population. The model describes the dynamics of cell densities, driven by pressureexclusion and cell proliferation. It has been shown that solutions to this system of partialdifferential equations have the segregation property, meaning that two population initiallysegregated remain segregated. This work is devoted to the incompressible limit of suchsystem towards a free boundary Hele Shaw type model for two cell populations.
Date Issued
2020-03
Date Acceptance
2019-09-16
Citation
Networks and Heterogeneous Media, 2020, 15 (1), pp.57-85
ISSN
1556-1801
Publisher
American Institute of Mathematical Sciences
Start Page
57
End Page
85
Journal / Book Title
Networks and Heterogeneous Media
Volume
15
Issue
1
Sponsor
The Royal Society
Engineering & Physical Science Research Council (EPSRC)
Engineering & Physical Science Research Council (EPSRC)
Engineering & Physical Science Research Council (EPSRC)
Identifier
https://www.aimsciences.org/article/doi/10.3934/nhm.2020003
Grant Number
WM130048
EP/M006883/1
EP/N014529/1
EP/P013651/1
Subjects
Science & Technology
Physical Sciences
Mathematics, Interdisciplinary Applications
Mathematics
Tissue growth
Two cell populations
Incompressible limit
Free boundary problem
SOLID TUMOR-GROWTH
INTERACTING POPULATIONS
SPATIAL SEGREGATION
BOUNDARY-PROBLEM
STABILITY
DISPERSE
math.AP
math.AP
35K55, 35R35, 65M08, 92C15, 92C10
Applied Mathematics
Publication Status
Published online
Date Publish Online
2019-12-01