Stability of partially congested travelling wave solutions for the extended Aw-Rascle system - Institut de Mathématiques de Marseille 2014- Access content directly
Preprints, Working Papers, ... Year : 2024

Stability of partially congested travelling wave solutions for the extended Aw-Rascle system

Abstract

We prove the non-linear stability of a class of travelling-wave solutions to the extended Aw-Rascle system with a singular offset function, which is formally equivalent to the compressible pressureless Navier-Stokes system with a singular viscosity. These solutions encode the effect of congestion by connecting a congested left state to an uncongested right state, and may also be viewed as approximations of solutions to the ‘hard-congestion model’. By using carefully weighted energy estimates we are able to prove the non-linear stability of viscous shock waves to the Aw-Rascle system under a small zero integral perturbation, which in particular extends previous results that do not handle the case where the viscosity is singular.
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Dates and versions

hal-04560792 , version 1 (26-04-2024)

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  • HAL Id : hal-04560792 , version 1

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Emile Deleage, Muhammed Ali Mehmood. Stability of partially congested travelling wave solutions for the extended Aw-Rascle system. 2024. ⟨hal-04560792⟩
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