The particle paths of hyperbolic conservation laws
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2023
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866909156398596096 |
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| author | Fjordholm, Ulrik S. Mæhlen, Ola H. Ørke, Magnus C. |
| author_facet | Fjordholm, Ulrik S. Mæhlen, Ola H. Ørke, Magnus C. |
| contents | Nonlinear scalar conservation laws are traditionally viewed as transport equations. We take instead the viewpoint of these PDEs as continuity equations with an implicitly defined velocity field. We show that a weak solution is the entropy solution if and only if the ODE corresponding to its velocity field is well-posed. We also show that the flow of the ODE is $1/2$-Hölder regular. Finally, we give several examples showing that our results are sharp, and we provide explicit computations in the case of a Riemann problem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_10885 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | The particle paths of hyperbolic conservation laws Fjordholm, Ulrik S. Mæhlen, Ola H. Ørke, Magnus C. Analysis of PDEs 34A36, 35A02, 35L65 Nonlinear scalar conservation laws are traditionally viewed as transport equations. We take instead the viewpoint of these PDEs as continuity equations with an implicitly defined velocity field. We show that a weak solution is the entropy solution if and only if the ODE corresponding to its velocity field is well-posed. We also show that the flow of the ODE is $1/2$-Hölder regular. Finally, we give several examples showing that our results are sharp, and we provide explicit computations in the case of a Riemann problem. |
| title | The particle paths of hyperbolic conservation laws |
| topic | Analysis of PDEs 34A36, 35A02, 35L65 |
| url | https://arxiv.org/abs/2306.10885 |