Scalar conservation laws seen as gradient flows: known results and new perspectives
We review some results in the literature which attempted (only partly successfully) at linking the theory of scalar conservation laws with the Wasserstein gradient flow theory. In particular, we consider the problem of writing a scalar conservation law within the Wasserstein gradient flow theory. As...
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| Format: | Article |
| Language: | English |
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EDP Sciences
2016-06-01
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| Series: | ESAIM: Proceedings and Surveys |
| Online Access: | https://doi.org/10.1051/proc/201654018 |
| _version_ | 1797972034633859072 |
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| author | Di Francesco Marco |
| author_facet | Di Francesco Marco |
| author_sort | Di Francesco Marco |
| collection | DOAJ |
| description | We review some results in the literature which attempted (only partly successfully) at linking the theory of scalar conservation laws with the Wasserstein gradient flow theory. In particular, we consider the problem of writing a scalar conservation law within the Wasserstein gradient flow theory. As a related problem, we also review results on contraction properties of scalar conservation laws in the p-Wasserstein distances. Moreover, we provide a particle-based approach to view a scalar conservation law as a gradient flow in a nonlinear-mobility sense. Finally, we propose a semi-implicit particle method based on the standard 2-Wasserstein distance. |
| first_indexed | 2024-04-11T03:40:55Z |
| format | Article |
| id | doaj.art-5089b05b8ba34a5b9f08540a7f6853db |
| institution | Directory Open Access Journal |
| issn | 2267-3059 |
| language | English |
| last_indexed | 2024-04-11T03:40:55Z |
| publishDate | 2016-06-01 |
| publisher | EDP Sciences |
| record_format | Article |
| series | ESAIM: Proceedings and Surveys |
| spelling | doaj.art-5089b05b8ba34a5b9f08540a7f6853db2023-01-02T03:40:02ZengEDP SciencesESAIM: Proceedings and Surveys2267-30592016-06-0154184410.1051/proc/201654018proc165402Scalar conservation laws seen as gradient flows: known results and new perspectivesDi Francesco MarcoWe review some results in the literature which attempted (only partly successfully) at linking the theory of scalar conservation laws with the Wasserstein gradient flow theory. In particular, we consider the problem of writing a scalar conservation law within the Wasserstein gradient flow theory. As a related problem, we also review results on contraction properties of scalar conservation laws in the p-Wasserstein distances. Moreover, we provide a particle-based approach to view a scalar conservation law as a gradient flow in a nonlinear-mobility sense. Finally, we propose a semi-implicit particle method based on the standard 2-Wasserstein distance.https://doi.org/10.1051/proc/201654018 |
| spellingShingle | Di Francesco Marco Scalar conservation laws seen as gradient flows: known results and new perspectives ESAIM: Proceedings and Surveys |
| title | Scalar conservation laws seen as gradient flows: known results and new perspectives |
| title_full | Scalar conservation laws seen as gradient flows: known results and new perspectives |
| title_fullStr | Scalar conservation laws seen as gradient flows: known results and new perspectives |
| title_full_unstemmed | Scalar conservation laws seen as gradient flows: known results and new perspectives |
| title_short | Scalar conservation laws seen as gradient flows: known results and new perspectives |
| title_sort | scalar conservation laws seen as gradient flows known results and new perspectives |
| url | https://doi.org/10.1051/proc/201654018 |
| work_keys_str_mv | AT difrancescomarco scalarconservationlawsseenasgradientflowsknownresultsandnewperspectives |