On the Aw-Rascle-Zhang traffic models with nonlocal look-ahead interactions
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866913264103849984 |
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| author | Hamori, Thomas Tan, Changhui |
| author_facet | Hamori, Thomas Tan, Changhui |
| contents | We present a new family of second-order traffic flow models, extending the Aw-Rascle-Zhang (ARZ) model to incorporate nonlocal interactions. Our model includes a specific nonlocal Arrhenius-type look-ahead slowdown factor. We establish both local and global well-posedness theories for these nonlocal ARZ models.
In contrast to the local ARZ model, where generic smooth initial data typically lead to finite-time shock formation, we show that our nonlocal ARZ model exhibits global regularity for a class of smooth subcritical initial data. Our result highlights the potential of nonlocal interactions to mitigate shock formations in second-order traffic flow models.
Our analytical approach relies on investigating phase plane dynamics. We introduce a novel comparison principle based on a mediant inequality to effectively handle the nonlocal information inherent in our model. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_08643 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the Aw-Rascle-Zhang traffic models with nonlocal look-ahead interactions Hamori, Thomas Tan, Changhui Analysis of PDEs 76A30, 35L65, 35B65, 35B51 We present a new family of second-order traffic flow models, extending the Aw-Rascle-Zhang (ARZ) model to incorporate nonlocal interactions. Our model includes a specific nonlocal Arrhenius-type look-ahead slowdown factor. We establish both local and global well-posedness theories for these nonlocal ARZ models. In contrast to the local ARZ model, where generic smooth initial data typically lead to finite-time shock formation, we show that our nonlocal ARZ model exhibits global regularity for a class of smooth subcritical initial data. Our result highlights the potential of nonlocal interactions to mitigate shock formations in second-order traffic flow models. Our analytical approach relies on investigating phase plane dynamics. We introduce a novel comparison principle based on a mediant inequality to effectively handle the nonlocal information inherent in our model. |
| title | On the Aw-Rascle-Zhang traffic models with nonlocal look-ahead interactions |
| topic | Analysis of PDEs 76A30, 35L65, 35B65, 35B51 |
| url | https://arxiv.org/abs/2403.08643 |