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- W4300174229 abstract "In the spirit of the macroscopic crowd motion models with hard congestion (i.e. a strong density constraint $rholeq 1$) introduced by Maury {it et al.} some years ago, we analyze a variant of the same models where diffusion of the agents is also taken into account. From the modeling point of view, this means that individuals try to follow a given spontaneous velocity, but are subject to a Brownian diffusion, and have to adapt to a density constraint which introduces a pressure term affecting the movement. From the PDE point of view, this corresponds to a modified Fokker-Planck equation, with an additional gradient of a pressure (only living in the saturated zone ${rho=1}$) in the drift. The paper proves existence and some estimates, based on optimal transport techniques." @default.
- W4300174229 created "2022-10-03" @default.
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- W4300174229 date "2015-03-08" @default.
- W4300174229 modified "2023-09-30" @default.
- W4300174229 title "Advection-diffusion equations with density constraints" @default.
- W4300174229 doi "https://doi.org/10.48550/arxiv.1503.02311" @default.
- W4300174229 hasPublicationYear "2015" @default.
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