2024/04/26 by Emile Deleage, Deléage, Émile, Muhammed Ali Mehmood +1
Mathematics · Physics and Astronomy · #35B25 #35L67 #35Q35 #76T20 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Photonic Systems #Nonlinear Waves and Solitons
paper · pdf · doi:10.48550/arxiv.2404.17406
openalex publication_date 2024/04/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.