73 citations · 240 across the 27 of their papers we have counts for
19 papers · 1 filter
Self-regulated biological transportation structures with general entropy dissipations, part I: the 1D case
Clarissa Astuto, Jan Haskovec, Peter Markowich +1
We study self-regulating processes modeling biological transportation networks as presented in \cite{portaro2023}. In particular, we focus on the 1D setting for Dirichlet and Neuma…
Optimal condition for asymptotic consensus in the Hegselmann-Krause model with finite speed of information propagation
Jan Haskovec, Mauro Rodriguez Cartabia
We prove that asymptotic global consensus is always reached in the Hegselmann-Krause model with finite speed of information propagation under minimal (i.e., necess…
Emergence of biological transportation networks as a self-regulated process
Jan Haskovec, Peter Markowich, Simone Portaro
We study self-regulating processes modeling biological transportation networks. Firstly, we write the formal -gradient flow for the symmetric tensor valued diffusivity of…
Cucker-Smale model with finite speed of information propagation: well-posedness, flocking and mean-field limit
Jan Haskovec
We study a variant of the Cucker-Smale model where information between agents propagates with a finite speed . This leads to a system of functional differential equ…
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…
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…
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…
Hydrodynamic Cucker-Smale model with normalized communication weights and time delay
Young-Pil Choi, Jan Haskovec
We study a hydrodynamic Cucker-Smale-type model with time delay in communication and information processing, in which agents interact with each other through normalized communicati…
Well posedness and Maximum Entropy Approximation for the Dynamics of Quantitative Traits
Katarina Bodova, Jan Haskovec, Peter Markowich
We study the Fokker-Planck equation derived in the large system limit of the Markovian process describing the dynamics of quantitative traits. The Fokker-Planck equation is posed o…
Cucker-Smale model with normalized communication weights and time delay
Young-Pil Choi, Jan Haskovec
We study a Cucker-Smale-type system with time delay in which agents interact with each other through normalized communication weights. We construct a Lyapunov functional for the sy…
Decay to equilibrium for energy-reaction-diffusion systems
Jan Haskovec, Sabine Hittmeir, Peter Markowich +1
We derive thermodynamically consistent models of reaction-diffusion equations coupled to a heat equation. While the total energy is conserved, the total entropy serves as a driving…
Notes on a PDE System for Biological Network Formation
Jan Haskovec, Peter Markowich, Benoit Perthame +1
We present new analytical and numerical results for the elliptic-parabolic system of partial differential equations proposed by Hu and Cai, which models the formation of biological…
Mathematical Analysis of a System for Biological Network Formation
Jan Haskovec, Peter Markowich, Benoit Perthame
Motivated by recent physics papers describing rules for natural network formation, we study an elliptic-parabolic system of partial differential equations proposed by Hu and Cai. T…
Consistency of Variational Continuous-Domain Quantization via Kinetic Theory
Massimo Fornasier, Jan Haskovec, Gabriele Steidl
We study the kinetic mean-field limits of the discrete systems of interacting particles used for halftoning of images in the sense of continuous-domain quantization. Under mild ass…
From individual to collective behaviour of coupled velocity jump processes: a locust example
Radek Erban, Jan Haskovec
A class of stochastic individual-based models, written in terms of coupled velocity jump processes, is presented and analysed. This modelling approach incorporates recent experimen…