37 citations · 91 across the 23 of their papers we have counts for
28 papers
Incompressible limit for a two-species Brinkman model with drift
Tomasz Dębiec, Valentin Vincent Neumann, Markus Schmidtchen
We study a two-species model for tissue growth in which both populations are transported by an external drift and by a velocity potential determined through Brinkman's law. The pre…
Convergence of a discrete-in-time Approximation to a Degenerate Parabolic-Hyperbolic System
Julia Hauser, Hideki Murakawa, Markus Schmidtchen
In this paper we consider an implicit semi-discrete approximation of a degenerate reaction-cross-diffusion system. Due to the symmetry in the parabolic part, this system is known t…
Convergence of a finite volume scheme for a model for ants
Maria Bruna, Markus Schmidtchen, Oscar de Wit
We develop and analyse a finite volume scheme for a nonlocal active matter system known to exhibit a rich array of complex behaviours. The model under investigation was derived fro…
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…