73 citations · 240 across the 27 of their papers we have counts for
32 papers
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…
Asymmetry and condition number of an elliptic-parabolic system for biological network formation
Clarissa Astuto, Daniele Boffi, Jan Haskovec +2
We present results of numerical simulations of the tensor-valued elliptic-parabolic PDE model for biological network formation. The numerical method is based on a non-linear finite…
Comparison of two aspects of a PDE model for biological network formation
Clarissa Astuto, Daniele Boffi, Jan Haskovec +2
We compare the solutions of two systems of partial differential equations (PDE), seen as two different interpretations of the same model that describes formation of complex biologi…
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…
Asymptotic behavior of the linear consensus model with delay and anticipation
Jan Haskovec
We study asymptotic behavior of solutions of the first-order linear consensus model with delay and anticipation, which is a system of neutral delay differential equations. We consi…
Direct proof of unconditional asymptotic consensus in the Hegselmann-Krause model with transmission-type delay
Jan Haskovec
We present a direct proof of asymptotic consensus in the nonlinear Hegselmann-Krause model with transmission-type delay, where the communication weights depend on the particle dist…
A simple proof of asymptotic consensus in the Hegselmann-Krause and Cucker-Smale models with renormalization and delay
Jan Haskovec
We present a simple proof of asymptotic consensus in the discrete Hegselmann-Krause model and flocking in the discrete Cucker-Smale model with renormalization and variable delay. I…
Exponential asymptotic flocking in the Cucker-Smale model with distributed reaction delays
Jan Haskovec, Ioannis Markou
We study a variant of the Cucker-Smale system with distributed reaction delays. Using backward-forward and stability estimates on the quadratic velocity fluctuations we derive suff…
Exponential decay for negative feedback loop with distributed delay
Jan Haskovec
We derive sufficient conditions for exponential decay of solutions of the delay negative feedback equation with distributed delay. The conditions are written in terms of exponentia…
Well posedness and asymptotic consensus in the Hegselmann-Krause model with finite speed of information propagation
Jan Haskovec
We consider a variant of the Hegselmann-Krause model of consensus formation where information between agents propagates with a finite speed . This leads to a system o…
Asymptotic and exponential decay in mean square for delay geometric Brownian motion
Jan Haskovec
We derive sufficient conditions for asymptotic and monotone exponential decay in mean square of solutions of the geometric Brownian motion with delay. The conditions are written in…
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…
Auxin transport model for leaf venation
Jan Haskovec, Henrik Jönsson, Lisa Maria Kreusser +1
The plant hormone auxin controls many aspects of the development of plants. One striking dynamical feature is the self-organisation of leaf venation patterns which is driven by hig…
Asymptotic flocking in the Cucker-Smale model with reaction-type delays in the non-oscillatory regime
Jan Haskovec, Ioannis Markou
We study a variant of the Cucker-Smale system with reaction-type delay. Using novel backward-forward and stability estimates on appropriate quantities we derive sufficient conditio…
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…