23 citations · 106 across the 22 of their papers we have counts for
6 papers · 1 filter
On anisotropic diffusion equations for label propagation
Lisa Maria Kreusser, Marie-Therese Wolfram
In many problems in data classification one wishes to assign labels to points in a point cloud with a certain number of them being already correctly labeled. In this paper, we prop…
Equilibria of an anisotropic nonlocal interaction equation: Analysis and numerics
José A. Carrillo, Bertram Düring, Lisa Maria Kreusser +1
In this paper, we study the equilibria of an anisotropic, nonlocal aggregation equation with nonlinear diffusion which does not possess a gradient flow structure. Here, the anisotr…
Rigorous Continuum Limit for the Discrete Network Formation Problem
Jan Haskovec, Lisa Maria Kreusser, Peter Markowich
Motivated by recent physics papers describing the formation of biological transport networks we study a discrete model proposed by Hu and Cai consisting of an energy consumption fu…
ODE and PDE based modeling of biological transportation networks
Jan Haskovec, Lisa Maria Kreusser, Peter Markowich
We study the global existence of solutions of a discrete (ODE based) model on a graph describing the formation of biological transportation networks, introduced by Hu and Cai. We p…
Pattern formation of a nonlocal, anisotropic interaction model
Martin Burger, Bertram Düring, Lisa Maria Kreusser +2
We consider a class of interacting particle models with anisotropic, repulsive-attractive interaction forces whose orientations depend on an underlying tensor field. An example of…
Trend to equilibrium for a delay Vlasov-Fokker-Planck equation and explicit decay estimates
Axel Klar, Lisa Kreusser, Oliver Tse
In this paper, a delay Vlasov-Fokker-Planck equation associated to a stochastic interacting particle system with delay is investigated analytically. Under certain restrictions on t…