Existence result for a 2 x 2 system of conservation laws with discontinuous flux and applications
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866917354352410624 |
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| author | Chiarello, Felisia Angela Fagioli, Simone Rosini, Massimiliano Daniele |
| author_facet | Chiarello, Felisia Angela Fagioli, Simone Rosini, Massimiliano Daniele |
| contents | This paper is concerned with one-dimensional 2 x 2 systems of conservation laws with a flux f=f(x, U) that is discontinuous with respect to the spatial variable. No monotonicity assumption is imposed on the mapping x \to f(x,U). We introduce a Kruzhkov-type entropy condition and establish the global existence of entropy solutions for large data. The proof relies on a wave-front tracking approximation. The main technical novelty consists in the introduction of adapted Riemann invariant coordinates, specifically designed to account for the discontinuities of the flux, which yield a uniform-in-time bound on the total variation of the approximate solutions U^n(t). We also outline several alternative approaches that may lead to existence results under possibly weaker assumptions. As an application, we propose second-order vehicular traffic models on inhomogeneous roads featuring abrupt ''collective'' changes in the speed law or road capacity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_12531 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Existence result for a 2 x 2 system of conservation laws with discontinuous flux and applications Chiarello, Felisia Angela Fagioli, Simone Rosini, Massimiliano Daniele Analysis of PDEs Primary: 35L65, 35L45, 35A01, Secondary: 90B20 This paper is concerned with one-dimensional 2 x 2 systems of conservation laws with a flux f=f(x, U) that is discontinuous with respect to the spatial variable. No monotonicity assumption is imposed on the mapping x \to f(x,U). We introduce a Kruzhkov-type entropy condition and establish the global existence of entropy solutions for large data. The proof relies on a wave-front tracking approximation. The main technical novelty consists in the introduction of adapted Riemann invariant coordinates, specifically designed to account for the discontinuities of the flux, which yield a uniform-in-time bound on the total variation of the approximate solutions U^n(t). We also outline several alternative approaches that may lead to existence results under possibly weaker assumptions. As an application, we propose second-order vehicular traffic models on inhomogeneous roads featuring abrupt ''collective'' changes in the speed law or road capacity. |
| title | Existence result for a 2 x 2 system of conservation laws with discontinuous flux and applications |
| topic | Analysis of PDEs Primary: 35L65, 35L45, 35A01, Secondary: 90B20 |
| url | https://arxiv.org/abs/2411.12531 |