5 papers
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…
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 consi…
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…
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.…