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...
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
EDP Sciences
2018-01-01
|
| Series: | ESAIM: Proceedings and Surveys |
| Online Access: | https://doi.org/10.1051/proc/201864137 |
| Summary: | 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. |
|---|---|
| ISSN: | 2267-3059 |