Zu Chongzhi Center Mathematics Research Seminar

Date and Time (China standard time): Monday, October 24, 8:00-9:00pm

Zoom ID: 912 3171 6061

Passcode: dkumath

Title: Incompressible limit and rate of convergence for tumor growth models with drift

Speaker: Noemi David

Bio: Noemi David got her PhD from Sorbonne University, she is currently a postdoc at Camille Jordan Institute, Université Lyon 1. Her research interests are parabolic partial differential equations and singular limits in tissue growth models.

Abstract: Both compressible and incompressible porous medium models have been used in the literature to describe the mechanical aspects of living tissues. Using a stiff pressure law, it is possible to build a link between these two different representations. In the incompressible limit, compressible models generate free boundary problems of Hele-Shaw type where saturation holds in the moving domain. In this talk, I will present the study of the incompressible limit for advection-porous medium equations motivated by tumor development. The derivation of the pressure equation in the stiff limit was an open problem for which the strong compactness of the pressure gradient is needed. To establish it, we use two new ideas: an L 3 -version of the celebrated Aronson-B´enilan estimate, also recently applied to related problems, and a sharp uniform L 4 -bound on the pressure gradient. Moreover, we provide an estimate of the convergence rate at the incompressible limit in a Sobolev negative norm.