On the multiscale modeling of vehicular traffic: from kinetic to hydrodynamics
From MaRDI portal
Publication:478679
DOI10.3934/dcdsb.2014.19.1869zbMath1302.35372OpenAlexW2326955160MaRDI QIDQ478679
Abdelghani Bellouquid, Juan Soler, Juanjo Nieto, Nicola Bellomo
Publication date: 4 December 2014
Published in: Discrete and Continuous Dynamical Systems. Series B (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.3934/dcdsb.2014.19.1869
Hyperbolic conservation laws (35L65) PDEs in connection with game theory, economics, social and behavioral sciences (35Q91) PDEs in connection with mechanics of particles and systems of particles (35Q70)
Related Items (25)
Cooperation, competition, organization: The dynamics of interacting living populations ⋮ Behavioral crowds: modeling and Monte Carlo simulations toward validation ⋮ Traveling waves for a microscopic model of traffic flow ⋮ Asymptotic problems and numerical schemes for traffic flows with unilateral constraints describing the formation of jams ⋮ Heterogeneous population dynamics of active particles: Progression, mutations, and selection dynamics ⋮ Traveling wave profiles for a follow-the-leader model for traffic flow with rough road condition ⋮ A unified multiscale vision of behavioral crowds ⋮ Macroscopic First Order Models of Multicomponent Human Crowds with Behavioral Dynamics ⋮ Tuned communicability metrics in networks. The case of alternative routes for urban traffic ⋮ Challenges in active particles methods: Theory and applications ⋮ Solutions to aggregation–diffusion equations with nonlinear mobility constructed via a deterministic particle approximation ⋮ Well-Posedness for Scalar Conservation Laws with Moving Flux Constraints ⋮ A multiscale model of cell mobility: from a kinetic to a hydrodynamic description ⋮ ODE-PDE models in traffic flow dynamics ⋮ Developing an Aw-Rascle model of traffic flow ⋮ Kinetic models of chemotaxis towards the diffusive limit: asymptotic analysis ⋮ On the interaction between soft and hard sciences: the role of mathematical sciences. Looking ahead to research perspectives ⋮ An asymptotic preserving scheme for kinetic models for chemotaxis phenomena ⋮ Fluid models with phase transition for kinetic equations in swarming ⋮ A multiscale view of nonlinear diffusion in biology: From cells to tissues ⋮ Vehicular traffic, crowds, and swarms: From kinetic theory and multiscale methods to applications and research perspectives ⋮ A macroscopic traffic model based on driver physiological response ⋮ Toward a mathematical theory of Keller–Segel models of pattern formation in biological tissues ⋮ Rigorous derivation of nonlinear scalar conservation laws from follow-the-leader type models via many particle limit ⋮ Euler-type equations and commutators in singular and hyperbolic limits of kinetic Cucker–Smale models
Cites Work
- On a class of integro-differential equations modeling complex systems with nonlinear interactions
- Hyperbolic and kinetic models for self-organized biological aggregations and movement: a brief review
- On the mathematical theory of vehicular traffic flow. II: Discrete velocity kinetic models
- Asymptotic limits of a discrete kinetic theory model of vehicular traffic
- Global solution to the Cauchy problem for discrete velocity models of vehicular traffic
- Nonlinear hydrodynamic models of traffic flow modelling and mathematical problems
- Coupling of non-local driving behaviour with fundamental diagrams
- On the mathematical theory of living systems. II: The interplay between mathematics and system biology
- Vehicular traffic: From microscopic to macroscopic description
- ON THE DIFFICULT INTERPLAY BETWEEN LIFE, "COMPLEXITY", AND MATHEMATICAL SCIENCES
- TOWARDS THE MODELING OF VEHICULAR TRAFFIC AS A COMPLEX SYSTEM: A KINETIC THEORY APPROACH
- ON THE MATHEMATICAL THEORY OF THE DYNAMICS OF SWARMS VIEWED AS COMPLEX SYSTEMS
- On the Modeling of Traffic and Crowds: A Survey of Models, Speculations, and Perspectives
- Derivation of Continuum Traffic Flow Models from Microscopic Follow-the-Leader Models
- MODELING CROWD DYNAMICS FROM A COMPLEX SYSTEM VIEWPOINT
- A derivation of the Aw–Rascle traffic models from Fokker–Planck type kinetic models
- Kinetic Derivation of Macroscopic Anticipation Models for Vehicular Traffic
- GENERALIZED KINETIC (BOLTZMANN) MODELS: MATHEMATICAL STRUCTURES AND APPLICATIONS
- Resurrection of "Second Order" Models of Traffic Flow
- MATHEMATICAL MODELING OF VEHICULAR TRAFFIC: A DISCRETE KINETIC THEORY APPROACH
This page was built for publication: On the multiscale modeling of vehicular traffic: from kinetic to hydrodynamics