4 papers · 1 filter
Nonlocal approximation of an anisotropic cross-diffusion system
Tomasz DÄbiec, Markus Schmidtchen
Localisation limits and nonlocal approximations of degenerate parabolic systems have experienced a renaissance in recent years. However, only few results cover anisotropic systems.…
From Finite to Continuous Phenotypes in (Visco-)Elastic Tissue Growth Models
Tomasz DÄbiec, Mainak Mandal, Markus Schmidtchen
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…
Uniform regularity estimates for nonlinear diffusion-advection equations in the hard-congestion limit
Noemi David, Filippo Santambrogio, Markus Schmidtchen
We present regularity results for nonlinear drift-diffusion equations of porous medium type (together with their incompressible limit). We relax the assumptions imposed on the drif…
Linking discrete and continuous models of cell birth and migration
W. Duncan Martinson, Alexandria Volkening, Markus Schmidtchen +2
Self-organisation of individuals within large collectives occurs throughout biology. Mathematical models can help elucidate the individual-level mechanisms behind these dynamics, b…