Nonlocal Generalized Aw-Rascle-Zhang model: well-posedness and singular limit
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arXiv
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| Format: | Preprint |
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2025
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| author | Marconi, Elio Spinolo, Laura V. |
| author_facet | Marconi, Elio Spinolo, Laura V. |
| contents | We discuss a nonlocal version of the Generalized Aw-Rascle-Zhang model, a second-order vehicular traffic model where the empty road velocity is a Lagrangian marker governed by a transport equation. The evolution of the car density is described by a continuity equation where the drivers' velocity depends on both the empty road velocity and the convolution of the car density with an anisotropic kernel. We establish existence and uniqueness results. When the convolution kernel is replaced by a Dirac Delta, the nonlocal model formally boils down to the classical (local) Generalized Aw-Rascle-Zhang model, which consists of a conservation law coupled with a transport equation. In the case of exponential kernels, we establish convergence in the nonlocal-to-local limit by proving an Oleinik-type estimate for the convolution term. To the best of our knowledge, this is the first nonlocal-to-local limit result for a system of two non-decoupling equations with a nonlocal flux function. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_10102 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Nonlocal Generalized Aw-Rascle-Zhang model: well-posedness and singular limit Marconi, Elio Spinolo, Laura V. Analysis of PDEs 35L65 We discuss a nonlocal version of the Generalized Aw-Rascle-Zhang model, a second-order vehicular traffic model where the empty road velocity is a Lagrangian marker governed by a transport equation. The evolution of the car density is described by a continuity equation where the drivers' velocity depends on both the empty road velocity and the convolution of the car density with an anisotropic kernel. We establish existence and uniqueness results. When the convolution kernel is replaced by a Dirac Delta, the nonlocal model formally boils down to the classical (local) Generalized Aw-Rascle-Zhang model, which consists of a conservation law coupled with a transport equation. In the case of exponential kernels, we establish convergence in the nonlocal-to-local limit by proving an Oleinik-type estimate for the convolution term. To the best of our knowledge, this is the first nonlocal-to-local limit result for a system of two non-decoupling equations with a nonlocal flux function. |
| title | Nonlocal Generalized Aw-Rascle-Zhang model: well-posedness and singular limit |
| topic | Analysis of PDEs 35L65 |
| url | https://arxiv.org/abs/2505.10102 |