| Abstract: |
| I will discuss some approaches to mathematical modelling of living tissues, with application to tumour growth. In particular, I will describe recent results on the incompressible limit (or stiff-pressure limit) for a compressible model, building a bridge between density-based description and a geometric free-boundary problem by passing to the singular limit in the pressure law. We set out from a two-species advection-reaction system --- the cell densities are advected by the gradient of a chemical potential which satisfies the so-called Brinkman law, while the growth rate of each population is governed by a function of the joint population pressure.
In the limit problem the total population density is limited to a critical value and the pressure vanishes on unsaturated regions. |
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