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.
https://hal.inria.fr/hal-01257180
Contributeur : Tommaso Lorenzi
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Soumis le : vendredi 6 janvier 2017 - 19:03:48
Dernière modification le : vendredi 4 janvier 2019 - 17:33:38
Document(s) archivé(s) le : vendredi 7 avril 2017 - 17:30:22
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-01257180v2〉
