70 citations · 239 across the 42 of their papers we have counts for
4 papers · 2 filters
Gradient flows on metric graphs with reservoirs: Microscopic derivation and multiscale limits
Georg Heinze, Jan-Frederik Pietschmann, André Schlichting
We study evolution equations on metric graphs with reservoirs, that is graphs where a one-dimensional interval is associated to each edge and, in addition, the vertices are able to…
Existence and local asymptotics for a system of cross-diffusion equations with nonlocal Cahn-Hilliard terms
Elisa Davoli, Greta Marino, Jan-Frederik Pietschmann
We study a nonlocal Cahn-Hilliard model for a multicomponent mixture with cross-diffusion effects and degenerate mobility. The nonlocality is described by means of a symmetric sing…
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…
Optimal transport on gas networks
Ariane Fazeny, Martin Burger, Jan-Frederik Pietschmann
This paper models gas networks as metric graphs, with isothermal Euler equations at the edges, Kirchhoff's law at interior vertices and time-(in)dependent boundary conditions at bo…