Stability of partially congested travelling wave solutions for the extended Aw-Rascle system
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866909183039766528 |
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| author | Deléage, Émile Mehmood, Muhammed Ali |
| author_facet | Deléage, Émile Mehmood, Muhammed Ali |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_17406 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Stability of partially congested travelling wave solutions for the extended Aw-Rascle system Deléage, Émile Mehmood, Muhammed Ali Analysis of PDEs 35Q35, 35L67, 35B25, 76T20 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. |
| title | Stability of partially congested travelling wave solutions for the extended Aw-Rascle system |
| topic | Analysis of PDEs 35Q35, 35L67, 35B25, 76T20 |
| url | https://arxiv.org/abs/2404.17406 |