A nonlocal Aw-Rascle-Zhang system with linear pressure term
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866912889367953408 |
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| author | Amadori, Debora Chiarello, Felisia Angela Cipollone, Gianmarco |
| author_facet | Amadori, Debora Chiarello, Felisia Angela Cipollone, Gianmarco |
| contents | In this paper, we study a nonlocal extension of the Aw-Rascle-Zhang traffic model, where the pressure-like term is modeled as a convolution between vehicle density and a kernel function. This formulation captures nonlocal driver interactions and aligns structurally with the Euler-alignment system studied in [23]. Using a sticky particle approximation, we construct entropy solutions to the equation for the cumulative density and prove convergence of approximate solutions to weak solutions of the nonlocal system. The analysis includes well-posedness, stability estimates, and an entropic selection principle. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_20973 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A nonlocal Aw-Rascle-Zhang system with linear pressure term Amadori, Debora Chiarello, Felisia Angela Cipollone, Gianmarco Analysis of PDEs 35D30, 35L65, 35Q92, 76N10, 35B30 In this paper, we study a nonlocal extension of the Aw-Rascle-Zhang traffic model, where the pressure-like term is modeled as a convolution between vehicle density and a kernel function. This formulation captures nonlocal driver interactions and aligns structurally with the Euler-alignment system studied in [23]. Using a sticky particle approximation, we construct entropy solutions to the equation for the cumulative density and prove convergence of approximate solutions to weak solutions of the nonlocal system. The analysis includes well-posedness, stability estimates, and an entropic selection principle. |
| title | A nonlocal Aw-Rascle-Zhang system with linear pressure term |
| topic | Analysis of PDEs 35D30, 35L65, 35Q92, 76N10, 35B30 |
| url | https://arxiv.org/abs/2509.20973 |