4 citations · 6 across the 6 of their papers we have counts for
8 papers · 1 filter
Tensor PDE model of biological network formation
Jan Haskovec, Peter Markowich, Giulia Pilli
We study an elliptic-parabolic system of partial differential equations describing formation of biological network structures. The model takes into consideration the evolution of t…
Flocking in the Cucker-Smale model with self-delay and nonsymmetric interaction weights
Jan Haskovec
We derive a sufficient condition for asymptotic flocking in the Cucker-Smale model with self-delay (also called reaction delay) and with non-symmetric interaction weights. The cond…
Murray's law for discrete and continuum models of biological networks
Jan Haskovec, Peter Markowich, Giulia Pilli
We demonstrate the validity of Murray's law, which represents a scaling relation for branch conductivities in a transportation network, for discrete and continuum models of biologi…
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…
A mesoscopic model of biological transportation networks
Martin Burger, Jan Haskovec, Peter Markowich +1
We introduce a mesoscopic model for natural network formation processes, acting as a bridge between the discrete and continuous network approach proposed by Hu and Cai. The models…
An Optimal Transport Approach for the Kinetic Bohmian Equation
Wilfrid Gangbo, Jan Haskovec, Peter Markowich +1
We study the existence theory of solutions of the kinetic Bohmian equation, a nonlinear Vlasov-type equation proposed for the phase-space formulation of Bohmian mechanics. Our main…