Stability of partially congested travelling wave solutions for the extended Aw-Rascle system
Analysis of PDEs
2024-04-29 v1
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.
Keywords
Cite
@article{arxiv.2404.17406,
title = {Stability of partially congested travelling wave solutions for the extended Aw-Rascle system},
author = {Émile Deléage and Muhammed Ali Mehmood},
journal= {arXiv preprint arXiv:2404.17406},
year = {2024}
}