Non-local traffic flow models with time delay: well-posedness and numerical approximation
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866910411929944064 |
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| author | Ciaramaglia, Ilaria Goatin, Paola Puppo, Gabriella |
| author_facet | Ciaramaglia, Ilaria Goatin, Paola Puppo, Gabriella |
| contents | We prove the well-posedness of weak entropy solutions of a scalar non-local traffic flow model with time delay. Existence is obtained by convergence of finite volume approximate solutions constructed by Lax-Friedrich and Hilliges-Weidlich schemes, while the L1 stability with respect to the initial data and the delay parameter relies on a Kruzkov-type doubling of variable technique.Numerical tests are provided to illustrate the efficiency of the proposed schemes, as well as the solution dependence on the delay and look-ahead parameters. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_10368 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Non-local traffic flow models with time delay: well-posedness and numerical approximation Ciaramaglia, Ilaria Goatin, Paola Puppo, Gabriella Analysis of PDEs Numerical Analysis We prove the well-posedness of weak entropy solutions of a scalar non-local traffic flow model with time delay. Existence is obtained by convergence of finite volume approximate solutions constructed by Lax-Friedrich and Hilliges-Weidlich schemes, while the L1 stability with respect to the initial data and the delay parameter relies on a Kruzkov-type doubling of variable technique.Numerical tests are provided to illustrate the efficiency of the proposed schemes, as well as the solution dependence on the delay and look-ahead parameters. |
| title | Non-local traffic flow models with time delay: well-posedness and numerical approximation |
| topic | Analysis of PDEs Numerical Analysis |
| url | https://arxiv.org/abs/2404.10368 |