Duality solutions to the hard-congestion model for the dissipative Aw-Rascle system
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arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866929242108854272 |
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| author | Chaudhuri, Nilasis Mehmood, Muhammed Ali Perrin, Charlotte Zatorska, Ewelina |
| author_facet | Chaudhuri, Nilasis Mehmood, Muhammed Ali Perrin, Charlotte Zatorska, Ewelina |
| contents | We introduce the notion of duality solution for the hard-congestion model on the real line, and additionally prove an existence result for this class of solutions. Our study revolves around the analysis of a generalised Aw-Rascle system, where the offset function is replaced by the gradient of a singular function, such as $ρ$ $γ$ n , where $γ$ $\rightarrow$ $\infty$. We prove that under suitable assumptions on the initial data, solutions to the Aw-Rascle system converge towards the so-called duality solutions, which have previously found applications in other systems which exhibit compressive dynamics. We also prove that one can obtain weak solutions to the limiting system under stricter assumptions on the initial data. Finally, we discuss (non-)uniqueness issues. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_08295 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Duality solutions to the hard-congestion model for the dissipative Aw-Rascle system Chaudhuri, Nilasis Mehmood, Muhammed Ali Perrin, Charlotte Zatorska, Ewelina Analysis of PDEs We introduce the notion of duality solution for the hard-congestion model on the real line, and additionally prove an existence result for this class of solutions. Our study revolves around the analysis of a generalised Aw-Rascle system, where the offset function is replaced by the gradient of a singular function, such as $ρ$ $γ$ n , where $γ$ $\rightarrow$ $\infty$. We prove that under suitable assumptions on the initial data, solutions to the Aw-Rascle system converge towards the so-called duality solutions, which have previously found applications in other systems which exhibit compressive dynamics. We also prove that one can obtain weak solutions to the limiting system under stricter assumptions on the initial data. Finally, we discuss (non-)uniqueness issues. |
| title | Duality solutions to the hard-congestion model for the dissipative Aw-Rascle system |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2402.08295 |