On interfaces between cell populations with different mobilities

Abstract : Partial differential equations describing the dynamics of cell population densities from a fluid mechanical perspective can model the growth of avascular tumours. In this framework, we consider a system of equations that describes the interaction between a population of dividing cells and a population of non-dividing cells. The two cell populations are characterised by different mobilities. We present the results of numerical simulations displaying two-dimensional spherical waves with sharp interfaces between dividing and non-dividing cells. Furthermore, we numerically observe how different ratios between the mobilities change the morphology of the interfaces, and lead to the emergence of finger-like patterns of invasion above a threshold. Motivated by these simulations, we study the existence of one-dimensional travelling wave solutions.
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https://hal.inria.fr/hal-01257180
Contributor : Tommaso Lorenzi <>
Submitted on : Friday, January 15, 2016 - 7:03:50 PM
Last modification on : Wednesday, November 20, 2019 - 4:16:01 PM
Long-term archiving on: Friday, November 11, 2016 - 8:20:05 AM

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  • HAL Id : hal-01257180, version 1

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Tommaso Lorenzi, Alexander Lorz, Benoît Perthame. On interfaces between cell populations with different mobilities. Kinetic and Related Models , AIMS, 2017, 10 (1), pp.299-311. ⟨hal-01257180v1⟩

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