Hard congestion limit of the dissipative Aw-Rascle system

N. Chaudhuri, L. Navoret, C. Perrin, E. Zatorska

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2 Scopus citations

Abstract

In this study, we analyse the famous Aw-Rascle system in which the difference between the actual and the desired velocities (the offset function) is a gradient of a singular function of the density. This leads to a dissipation in the momentum equation which vanishes when the density is zero. The resulting system of PDEs can be used to model traffic or suspension flows in one dimension with the maximal packing constraint taken into account. After proving the global existence of smooth solutions, we study the so-called ‘hard congestion limit’, and show the convergence of a subsequence of solutions towards a weak solution of a hybrid free-congested system. This is also illustrated numerically using a numerical scheme proposed for the model studied. In the context of suspension flows, this limit can be seen as the transition from a suspension regime, driven by lubrication forces, towards a granular regime, driven by the contacts between the grains.

Original languageEnglish (US)
Article number045018
JournalNonlinearity
Volume37
Issue number4
DOIs
StatePublished - Apr 1 2024

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • General Physics and Astronomy
  • Applied Mathematics

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