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math.NA2025
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…
math.AP2025
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…
math.AP2025
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…