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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Communicated by C. M. Dafermos
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Berthelin, F., Degond, P., Delitala, M. et al. A Model for the Formation and Evolution of Traffic Jams. Arch Rational Mech Anal 187, 185–220 (2008). https://doi.org/10.1007/s00205-007-0061-9
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DOI: https://doi.org/10.1007/s00205-007-0061-9