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Advection-diffusion equations with density constraints

Mészáros, Alpár Richárd; Santambrogio, Filippo

Authors

Filippo Santambrogio



Abstract

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.

Citation

Mészáros, A. R., & Santambrogio, F. (2016). Advection-diffusion equations with density constraints. Analysis & PDE, 9(3), 615-644. https://doi.org/10.2140/apde.2016.9.615

Journal Article Type Article
Acceptance Date Feb 9, 2016
Online Publication Date Jun 17, 2016
Publication Date 2016
Deposit Date Oct 1, 2019
Publicly Available Date Mar 28, 2024
Journal Analysis and PDE
Print ISSN 2157-5045
Electronic ISSN 2157-5045
Publisher Mathematical Sciences Publishers (MSP)
Peer Reviewed Peer Reviewed
Volume 9
Issue 3
Pages 615-644
DOI https://doi.org/10.2140/apde.2016.9.615
Related Public URLs https://arxiv.org/abs/1503.02311