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Pré-publication, Document de travail

Hard congestion limit of the dissipative Aw-Rascle system

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 an hybrid freecongested system. 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 contact between the grains.
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Pré-publication, Document de travail
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https://hal.archives-ouvertes.fr/hal-03786853
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Soumis le : vendredi 23 septembre 2022 - 16:57:27
Dernière modification le : mardi 27 septembre 2022 - 08:28:13

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CNPZ_2022.pdf
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  • HAL Id : hal-03786853, version 1

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Nilasis Chaudhuri, Laurent Navoret, Charlotte Perrin, Ewelina Zatorska. Hard congestion limit of the dissipative Aw-Rascle system. {date}. ⟨hal-03786853⟩

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