37 citations · 91 across the 23 of their papers we have counts for
5 papers · 1 filter
Nonlocal approximation of an anisotropic cross-diffusion system
Tomasz Dębiec, 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 Dębiec, 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…
Existence of weak solutions for a volume-filling model of cell invasion into extracellular matrix
Rebecca M. Crossley, Jan-Frederik Pietschmann, Markus Schmidtchen
We study the existence of weak solutions for a model of cell invasion into the extracellular matrix (ECM), which consists of a non-linear partial differential equation for the dens…
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…
The approximation of the quadratic porous medium equation via nonlocal interacting particles subject to repulsive Morse potential
Marco Di Francesco, Valeria Iorio, Markus Schmidtchen
We propose a deterministic particle method for a one-dimensional nonlocal equation with interactions through the repulsive Morse potential. We show that the particle method converg…