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AbstractPartial 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.
CitationLorenzi T, Lorz A, Perthame B (2016) On interfaces between cell populations with different mobilities. Kinetic and Related Models 10: 299–311. Available: http://dx.doi.org/10.3934/krm.2017012.
SponsorsThis work was supported in part by the French National Research Agency through the
JournalKinetic and Related Models