Fully discrete follow-the-leader approximation of one-dimensional scalar conservation laws with vacuum
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866912866821472256 |
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| author | Di Francesco, M. Fagioli, S. Iorio, V. Rosini, M. D. |
| author_facet | Di Francesco, M. Fagioli, S. Iorio, V. Rosini, M. D. |
| contents | We present a fully discrete particle approximation for one-dimensional scalar conservation laws. Under suitable monotonicity assumptions on the macroscopic velocity, we construct a vacuum-compatible family of time-discrete particle equations and show that an appropriate piecewise-constant density reconstruction from the particle setting converges to the unique entropy weak solution of the macroscopic scalar conservation law. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_01145 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Fully discrete follow-the-leader approximation of one-dimensional scalar conservation laws with vacuum Di Francesco, M. Fagioli, S. Iorio, V. Rosini, M. D. Analysis of PDEs 35L60, 35L03, 65M12, 76A30 We present a fully discrete particle approximation for one-dimensional scalar conservation laws. Under suitable monotonicity assumptions on the macroscopic velocity, we construct a vacuum-compatible family of time-discrete particle equations and show that an appropriate piecewise-constant density reconstruction from the particle setting converges to the unique entropy weak solution of the macroscopic scalar conservation law. |
| title | Fully discrete follow-the-leader approximation of one-dimensional scalar conservation laws with vacuum |
| topic | Analysis of PDEs 35L60, 35L03, 65M12, 76A30 |
| url | https://arxiv.org/abs/2602.01145 |