Geodesic
Crowd motion and evolution PDEs under density constraints
Filippo Santambrogio1
1 Laboratoire de Mathématiques d'Orsay, Univ. Paris-Sud, CNRS, Université Paris-Saclay, 91405 Orsay, FRANCE; filippo.santambrogio@math.u-psud.fr
ESAIM. Proceedings, Tome 64 (2018), pp. 137-157.

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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.
DOI : 10.1051/proc/201864137

Filippo Santambrogio 1

1 Laboratoire de Mathématiques d'Orsay, Univ. Paris-Sud, CNRS, Université Paris-Saclay, 91405 Orsay, FRANCE; filippo.santambrogio@math.u-psud.fr 
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     author = {Filippo Santambrogio},
     title = {Crowd motion and evolution {PDEs} under density constraints},
     journal = {ESAIM. Proceedings},
     pages = {137--157},
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     volume = {64},
     year = {2018},
     doi = {10.1051/proc/201864137},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/proc/201864137/}
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Filippo Santambrogio. Crowd motion and evolution PDEs under density constraints. ESAIM. Proceedings, Tome 64 (2018), pp. 137-157. doi : 10.1051/proc/201864137. http://geodesic.mathdoc.fr/articles/10.1051/proc/201864137/

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