Incompressible limit of a continuum model of tissue growth for two cell populations
Pierre Degond, Sophie Hecht, Nicolas Vauchelet
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.
Topics & Concepts
CompressibilityLimit (mathematics)PopulationBoundary (topology)Boundary value problemPartial differential equationMathematicsPhysicsWork (physics)Mathematical analysisMechanicsThermodynamicsDemographySociologyMathematical Biology Tumor GrowthMathematical and Theoretical Epidemiology and Ecology ModelsStochastic processes and financial applications