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arXiv · 2404.17406

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

Émile Deléage·Muhammed Ali Mehmood
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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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Émile Deléage, Muhammed Ali Mehmood. 2024-04-26. Stability of partially congested travelling wave solutions for the extended Aw-Rascle system. https://arxiv.org/abs/2404.17406

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