Macroscopic models for vehicular flows and crowd dynamics: theory and applications. Classical and non-classical advanced mathematics for real life applications

DOI10.1007/978-3-319-00155-5zbMath1284.35003OpenAlexW2491235687MaRDI QIDQ367283

Publication date: 26 September 2013

Published in: Understanding Complex Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-319-00155-5

zbMATH Keywords

singularities conservation laws balance laws congestion entropy weak solutions Braess' paradox for pedestrian flows equilibrium models Macroscopic flow models non-entropy weak solutions non-equilibrium models nonlinear hyperbolic balance laws rise of panic wave-front-tracking algorithm

Mathematics Subject Classification ID

Shocks and singularities for hyperbolic equations (35L67) Hyperbolic conservation laws (35L65) Traffic problems in operations research (90B20) Research exposition (monographs, survey articles) pertaining to partial differential equations (35-02)

Related Items (32)

Entropy solutions for a traffic model with phase transitions ⋮ Nonsmooth mean field games with state constraints ⋮ Solutions of the Aw-Rascle-Zhang system with point constraints ⋮ A macroscopic traffic model with phase transitions and local point constraints on the flow ⋮ Existence of \textbf{BV} solutions for a non-conservative constrained aw-rascle-Zhang model for vehicular traffic ⋮ Crowd dynamics and conservation laws with nonlocal constraints and capacity drop ⋮ Wavefronts in traffic flows and crowds dynamics ⋮ Multipopulation Minimal-Time Mean Field Games ⋮ Traveling waves for degenerate diffusive equations on networks ⋮ Coupling conditions for isothermal gas flow and applications to valves ⋮ Existence analysis and numerical approximation for a second-order model of traffic with orderliness marker ⋮ Viscous profiles in models of collective movement with negative diffusivity ⋮ Coherence and chattering of a one‐way valve ⋮ On existence, stability and many-particle approximation of solutions of 1D Hughes' model with linear costs ⋮ An all-densities pedestrian simulator based on a dynamic evaluation of the interpersonal distances ⋮ A Microscopic Model of Redistribution of Individuals Inside an ‘Elevator’ ⋮ A two-dimensional data-driven model for traffic flow on highways ⋮ Two time-varying and state-dependent fluid queuing models for traffic circulation systems ⋮ An existence result for a constrained two-phase transition model with metastable phase for vehicular traffic ⋮ Kinetic models for traffic flow resulting in a reduced space of microscopic velocities ⋮ Modeling crowd dynamics through coarse-grained data analysis ⋮ A second-order model for vehicular traffics with local point constraints on the flow ⋮ Convergence of the follow-the-leader scheme for scalar conservation laws with space dependent flux ⋮ Deterministic particle approximation of the Hughes model in one space dimension ⋮ Properties of the LWR model with time delay ⋮ Representation of capacity drop at a road merge via point constraints in a first order traffic model ⋮ Qualitative behaviour and numerical approximation of solutions to conservation laws with non-local point constraints on the flux and modeling of crowd dynamics at the bottlenecks ⋮ Wavefronts for degenerate diffusion-convection reaction equations with sign-changing diffusivity ⋮ On the motion of substance in a channel and growth of random networks ⋮ Attainable profiles for conservation laws with flux function spatially discontinuous at a single point ⋮ Traveling waves for conservation laws with cubic nonlinearity and BBM type dispersion ⋮ Rigorous derivation of nonlinear scalar conservation laws from follow-the-leader type models via many particle limit

This page was built for publication: Macroscopic models for vehicular flows and crowd dynamics: theory and applications. Classical and non-classical advanced mathematics for real life applications