Archive for Rational Mechanics and Analysis

, Volume 187, Issue 2, pp 185–220 | Cite as

A Model for the Formation and Evolution of Traffic Jams

Article

Abstract

In this paper, we establish and analyze a traffic flow model which describes the formation and dynamics of traffic jams. It consists of a pressureless gas dynamics system under a maximal constraint on the density and is derived through a singular limit of the Aw-Rascle model. From this analysis, we deduce the particular dynamical behavior of clusters (or traffic jams), defined as intervals where the density limit is reached. An existence result for a generic class of initial data is proved by means of an approximation of the solution by a sequence of clusters. Finally, numerical simulations are produced.

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Copyright information

© Springer-Verlag 2007

Authors and Affiliations

  • F. Berthelin
    • 1
  • P. Degond
    • 2
  • M. Delitala
    • 3
  • M. Rascle
    • 1
  1. 1.Laboratoire J. A. DieudonnéUniversité de NiceNiceFrance
  2. 2.MIP UMR 5640Université Paul SabatierToulouseFrance
  3. 3.Department of MathematicsPolitecnico di TorinoTorinoItaly

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