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Incompressible limit for a two-species model with coupling through Brinkmanâ s law. Dębiec, Tomasz

Description

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.

Joint work with B. Perthame (Sorbonne), M. Schmidtchen (TU Dresden) and N. Vauchelet (Paris 13).

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