Crowd motion and evolution PDEs under density constraints
This is a survey about the theory of density-constrained evolutions in theWasserstein space developed by B. Maury, the author, and their collaborators as a model for crowd motion. Connections with microscopic models and other PDEs are presented, as well as several time-discretization schemes based o...
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| Format: | Article |
| Language: | English |
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EDP Sciences
2018-01-01
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| Series: | ESAIM: Proceedings and Surveys |
| Online Access: | https://doi.org/10.1051/proc/201864137 |
| _version_ | 1797967737050365952 |
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| author | Santambrogio Filippo |
| author_facet | Santambrogio Filippo |
| author_sort | Santambrogio Filippo |
| collection | DOAJ |
| description | This is a survey about the theory of density-constrained evolutions in theWasserstein space developed by B. Maury, the author, and their collaborators as a model for crowd motion. Connections with microscopic models and other PDEs are presented, as well as several time-discretization schemes based on variational techniques, together with the main theorems guaranteeing their convergence as a tool to prove existence results. Then, a section is devoted to the uniqueness question, and a last one to different numerical methods inspired by optimal transport. |
| first_indexed | 2024-04-11T02:35:55Z |
| format | Article |
| id | doaj.art-ab74d47d71914fb1a941915a3b00eeef |
| institution | Directory Open Access Journal |
| issn | 2267-3059 |
| language | English |
| last_indexed | 2024-04-11T02:35:55Z |
| publishDate | 2018-01-01 |
| publisher | EDP Sciences |
| record_format | Article |
| series | ESAIM: Proceedings and Surveys |
| spelling | doaj.art-ab74d47d71914fb1a941915a3b00eeef2023-01-02T20:16:51ZengEDP SciencesESAIM: Proceedings and Surveys2267-30592018-01-016413715710.1051/proc/201864137proc186410Crowd motion and evolution PDEs under density constraintsSantambrogio FilippoThis is a survey about the theory of density-constrained evolutions in theWasserstein space developed by B. Maury, the author, and their collaborators as a model for crowd motion. Connections with microscopic models and other PDEs are presented, as well as several time-discretization schemes based on variational techniques, together with the main theorems guaranteeing their convergence as a tool to prove existence results. Then, a section is devoted to the uniqueness question, and a last one to different numerical methods inspired by optimal transport.https://doi.org/10.1051/proc/201864137 |
| spellingShingle | Santambrogio Filippo Crowd motion and evolution PDEs under density constraints ESAIM: Proceedings and Surveys |
| title | Crowd motion and evolution PDEs under density constraints |
| title_full | Crowd motion and evolution PDEs under density constraints |
| title_fullStr | Crowd motion and evolution PDEs under density constraints |
| title_full_unstemmed | Crowd motion and evolution PDEs under density constraints |
| title_short | Crowd motion and evolution PDEs under density constraints |
| title_sort | crowd motion and evolution pdes under density constraints |
| url | https://doi.org/10.1051/proc/201864137 |
| work_keys_str_mv | AT santambrogiofilippo crowdmotionandevolutionpdesunderdensityconstraints |