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Advection-diffusion equations with density constraints.

Mészáros, Alpár Richárd and Santambrogio, Filippo (2016) 'Advection-diffusion equations with density constraints.', Analysis & PDE., 9 (3). pp. 615-644.


In the spirit of the macroscopic crowd motion models with hard congestion (i.e., a strong density constraint ρ≤1) introduced by Maury 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 point of view of PDEs, this corresponds to a modified Fokker–Planck equation, with an additional gradient of a pressure (only living in the saturated zone {ρ=1}) in the drift. We prove existence and some estimates, based on optimal transport techniques.

Item Type:Article
Full text:Publisher-imposed embargo
(AM) Accepted Manuscript
File format - PDF (Copyright agreement prohibits open access to the full-text)
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Publisher statement:First published in Mészáros, Alpár Richárd & Santambrogio, Filippo (2016). Advection-diffusion equations with density constraints. Analysis & PDE 9(3): 615-644 published by Mathematical Sciences Publishers. © 2016 Mathematical Sciences Publishers. All rights reserved.
Date accepted:09 February 2016
Date deposited:28 February 2020
Date of first online publication:17 June 2016
Date first made open access:No date available

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