# On the incompressible limit of the porous media equation for some tumor growth models

## Location

Zoom: Please email Lenya Ryzhik (ryzhik@math.stanford.edu) to be added to seminar mailing list.

Wednesday, June 2, 2021 12:00 PM

Antoine Mellet (University of Maryland)

I will present some results on the incompressible limit of some porous media type equations that have been proposed as simple mechanical models for tumor growth. When the tumor can only grow, this limit gives rise to a free boundary problem of Hele-Shaw type, but we also consider (still simple) models that include mechanisms that cause the tumor to shrink (lack of nutrients for cancerous cell or drugs). Since the receding Hele-Shaw problem is famously ill-posed, new mathematical approaches are needed to describe the asymptotic model in geometric terms.