37 citations · 91 across the 23 of their papers we have counts for
4 papers · 1 filter
Gradient Flow Solutions For Porous Medium Equations with Nonlocal Lévy-type Pressure
Guy Foghem, David Padilla-Garza, Markus Schmidtchen
We study a porous medium-type equation whose pressure is given by a nonlocal Lévy operator associated to a symmetric jump Lévy kernel. The class of nonlocal operators under conside…
A Convergent Finite Volume Method for a Kinetic Model for Interacting Species
Julia I. M. Hauser, Valeria Iorio, Markus Schmidtchen
We propose an upwind finite volume method for a system of two kinetic equations in one dimension that are coupled through nonlocal interaction terms. These cross-interaction system…
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…
A Degenerate Cross-Diffusion System as the Inviscid Limit of a Nonlocal Tissue Growth Model
Noemi David, Tomasz Dębiec, Mainak Mandal +1
In recent years, there has been a spike in the interest in multi-phase tissue growth models. Depending on the type of tissue, the velocity is linked to the pressure through Stoke's…