On interfaces between cell populations with different mobilities
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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.
Lorenzi , T , Lorz , A & Perthame , B 2017 , ' On interfaces between cell populations with different mobilities ' , Kinetic and Related Models , vol. 10 , no. 1 , pp. 299-311 . https://doi.org/10.3934/krm.2017012
Kinetic and Related Models
© 2017, American Institute of Mathematical Sciences. This work is made available online in accordance with the publisher’s policies. This is the author created, accepted version manuscript following peer review and may differ slightly from the final published version. The final published version of this work is available at www.aimsciences.org / http://dx.doi.org/10.3934/krm.2017012
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