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Incompressible limit of a mechanical models for tissue growth

Presented by: 
Sophie Hecht
Tuesday 14th November 2017 - 11:00 to 11:30
INI Seminar Room 1
We consider mathematical models for tissue growth. These models describes the dynamics of the density of cells due to pressure forces and proliferation. It is known that some cell population models of this kind converge at the incompressible limit towards a Hele-Shaw type free boundary problem. The first model introduce a non-overlapping constraint of a population choosing a singular pressure law. The second model represents two interacting populations of cells which avoid mixing. Following earlier works, we show that the models approximate a free boundary Hele Shaw type model that we characterise using both analytical and numerical argument.
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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons