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Incompressible limit for a two-species tumour growth model

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Incompressible limit for a two-species tumour growth model
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Incompressible limit for a two-species model with coupling through Brinkmanâ s law.
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39
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CC Attribution - NonCommercial - NoDerivatives 4.0 International:
You are free to use, copy, distribute and transmit the work or content in unchanged form for any legal and non-commercial purpose as long as the work is attributed to the author in the manner specified by the author or licensor.
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Abstract
We study a two-species model of tissue growth describing dynamics under mechanical pressure and cell growth. The pressure is incorporated into the common fluid velocity through an elliptic equation, called Brinkmanâ s law, which accounts for viscosity effects in the individual species. Our aim is to establish the incompressible limit as the stiffness of the pressure law tends to infinity - thus demonstrating a rigorous bridge between the population dynamics of growing tissue at a density level and a geometric model thereof.
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