Both compressible and incompressible porous medium models are used in the literature to
describe the mechanical properties of living tissues. These two classes of models can be …

We complete previous results about the incompressible limit of both the n-dimensional (n≥
3) compressible Patlak-Keller-Segel (PKS) model and its stationary state. As in previous …

In this paper we study a cross-diffusion system whose coefficient matrix is non-symmetric
and degenerate. The system arises in the study of tissue growth with autophagy. The …

In recent years, there has been a spike in interest in multiphase tissue growth models.
Depending on the type of tissue, the velocity is linked to the pressure through Stoke's law …

We consider a (degenerate) cross-diffusion model of tumour growth structured by
phenotypic trait. We prove the existence of weak solutions and the incompressible limit as …

We revisit the problem of proving the incompressible limit for the compressible porous media
equation with Newtonian drift and growth. The question is motivated by models of living …

In this study, we explore a mathematical model for tissue growth focusing on the interplay
between multiple cell subpopulations with distinct phenotypic characteristics. The model …

Several recent papers have addressed modelling of the tissue growth by the multi-phase
models where the velocity is related to the pressure by one of the physical laws (Stoke's …

In a celebrated three-page-long paper in 1979, Aronson and Bénilan obtained a remarkable
estimate on second-order derivatives for the solution of the porous media equation. Since its …

Reaction cross diffusion systems are a two species generalization of the porous media
equation. These systems play an important role in the mechanical modeling of living tissues …