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  1. Nonlinear Differential Equations and Applications NoDEA
  2. Nonlinear Differential Equations and Applications NoDEA : Volume 21
  3. Nonlinear Differential Equations and Applications NoDEA : Volume 21, Issue 4, August 2014
  4. Invariance and homogenization of an adaptive time gap car-following model
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Nonlinear Differential Equations and Applications NoDEA : Volume 23
Nonlinear Differential Equations and Applications NoDEA : Volume 22
Nonlinear Differential Equations and Applications NoDEA : Volume 21
Nonlinear Differential Equations and Applications NoDEA : Volume 21, Issue 6, December 2014
Nonlinear Differential Equations and Applications NoDEA : Volume 21, Issue 5, October 2014
Nonlinear Differential Equations and Applications NoDEA : Volume 21, Issue 4, August 2014
Some remarks on quasilinear parabolic problems with singular potential and a reaction term
Invariance and homogenization of an adaptive time gap car-following model
An elliptic problem with an indefinite nonlinearity and a parameter in the boundary condition
Principal eigenvalue of the fractional Laplacian with a large incompressible drift
On the Fučik spectrum of non-local elliptic operators
Waiting time effect for motion by positive second derivatives and applications
Nonlinear Differential Equations and Applications NoDEA : Volume 21, Issue 3, June 2014
Nonlinear Differential Equations and Applications NoDEA : Volume 21, Issue 2, April 2014
Nonlinear Differential Equations and Applications NoDEA : Volume 21, Issue 1, February 2014
Nonlinear Differential Equations and Applications NoDEA : Volume 20
Nonlinear Differential Equations and Applications NoDEA : Volume 19
Nonlinear Differential Equations and Applications NoDEA : Volume 18
Nonlinear Differential Equations and Applications NoDEA : Volume 17
Nonlinear Differential Equations and Applications NoDEA : Volume 16
Nonlinear Differential Equations and Applications NoDEA : Volume 15
Nonlinear Differential Equations and Applications NoDEA : Volume 14
Nonlinear Differential Equations and Applications NoDEA : Volume 13
Nonlinear Differential Equations and Applications NoDEA : Volume 12
Nonlinear Differential Equations and Applications NoDEA : Volume 11
Nonlinear Differential Equations and Applications NoDEA : Volume 10
Nonlinear Differential Equations and Applications NoDEA : Volume 9
Nonlinear Differential Equations and Applications NoDEA : Volume 8
Nonlinear Differential Equations and Applications NoDEA : Volume 7
Nonlinear Differential Equations and Applications NoDEA : Volume 6
Nonlinear Differential Equations and Applications NoDEA : Volume 5
Nonlinear Differential Equations and Applications NoDEA : Volume 4

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Invariance and homogenization of an adaptive time gap car-following model

Content Provider SpringerLink
Author Tordeux, A. Roussigl, M. Monneau, R.
Copyright Year 2013
Abstract In this paper we consider a microscopic model of traffic flow called the adaptive time gap car-following model. This is a system of ODEs which describes the interactions between cars moving on a single line. The time gap is the time that a car needs to reach the position of the car in front of it (if the car in front of it would not move and if the moving car would not change its velocity). In this model, both the velocity of the car and the time gap satisfy an ODE. We study this model and show that under certain assumptions, there is an invariant set for which the dynamics is defined for all times and for which we have a comparison principle. As a consequence, we show rigorously that after rescaling, this microscopic model converges to a macroscopic model that can be identified as the classical LWR model for traffic.
Ending Page 517
Page Count 27
Starting Page 491
File Format PDF
ISSN 10219722
e-ISSN 14209004
Journal Nonlinear Differential Equations and Applications NoDEA
Issue Number 4
Volume Number 21
Language English
Publisher Springer Basel
Publisher Date 2013-11-13
Publisher Place Basel
Access Restriction One Nation One Subscription (ONOS)
Subject Keyword Hamilton-Jacobi equations Homogenization; equations in media with periodic structure Hamilton–Jacobi equation Car-following model Particle system Analysis Traffic Homogenization Infinite particle systems Nonlinear first-order equations Viscosity solutions
Content Type Text
Resource Type Article
Subject Applied Mathematics Analysis
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