23 citations · 106 across the 22 of their papers we have counts for
3 papers · 1 filter
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…
Stability analysis of line patterns of an anisotropic interaction model
José A. Carrillo, Bertram Düring, Lisa Maria Kreusser +1
Motivated by the formation of fingerprint patterns we consider a class of interacting particle models with anisotropic, repulsive-attractive interaction forces whose orientations d…
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…