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Hard congestion limit of the dissipative Aw–Rascle system
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Chaudhuri, N., Navoret, L., Perrin, C. and Zatorska, E. (2024) Hard congestion limit of the dissipative Aw–Rascle system. Nonlinearity, 37 (4). 045018. 045018. doi:10.1088/1361-6544/ad2b14 ISSN 0951-7715.
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Official URL: http://doi.org/10.1088/1361-6544/ad2b14
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.
Item Type: | Journal Article | ||||||
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Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||
Journal or Publication Title: | Nonlinearity | ||||||
Publisher: | Institute of Physics Publishing Ltd. | ||||||
ISSN: | 0951-7715 | ||||||
Official Date: | 14 March 2024 | ||||||
Dates: |
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Volume: | 37 | ||||||
Number: | 4 | ||||||
Page Range: | 045018 | ||||||
Article Number: | 045018 | ||||||
DOI: | 10.1088/1361-6544/ad2b14 | ||||||
Status: | Peer Reviewed | ||||||
Publication Status: | Published | ||||||
Access rights to Published version: | Open Access (Creative Commons) | ||||||
Date of first compliant deposit: | 9 April 2024 | ||||||
Date of first compliant Open Access: | 9 April 2024 |
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