mardi 21 mars 2023 à 13.15 - salle 109 (1er étage)
Noemi David (Laboratoire Jacques-Louis Lions)
Incompressible limit and rate of convergence for tumor growth models with drift
Both compressible and incompressible models of porous medium type 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 bridge between these two different representations. In the stiff-pressure 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 limit was an open problem for which the strong compactness of the pressure gradient was needed. Then, I will discuss the convergence rate of solutions of the compressible model to solutions of the Hele-Shaw problem.