Mean-field limit for collective behavior models with sharp sensitivity regions

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Title: Mean-field limit for collective behavior models with sharp sensitivity regions
Authors: Carrillo de la Plata, J
Choi, YP
Hauray, M
Salem, S
Item Type: Journal Article
Abstract: We rigorously show the mean-field limit for a large class of swarming individual based models with local sharp sensitivity regions. For instance, these models include nonlocal repulsive-attractive forces locally averaged over sharp vision cones and Cucker-Smale interactions with discontinuous communication weights. We construct global-in-time defined notion of solutions through a differential inclusion system corresponding to the particle descriptions. We estimate the error between the solutions to the differential inclusion system and weak solutions to the expected limiting kinetic equation by employing tools from optimal transport theory. Quantitative bounds on the expansion of the 1-Wasserstein distance along flows based on a weak-strong stability estimate are obtained. We also provide different examples of realistic sensitivity sets satisfying the assumptions of our main results.
Issue Date: 1-Jan-2019
Date of Acceptance: 3-May-2016
URI: http://hdl.handle.net/10044/1/32945
DOI: https://dx.doi.org/10.4171/JEMS/832
ISSN: 1435-9855
Publisher: European Mathematical Society
Start Page: 121
End Page: 161
Journal / Book Title: Journal of the European Mathematical Society
Volume: 21
Issue: 1
Copyright Statement: © 2018 EMS Publishing House. All rights reserved.
Sponsor/Funder: The Royal Society
Engineering & Physical Science Research Council (EPSRC)
Funder's Grant Number: WM120001
EP/K008404/1
Keywords: 0101 Pure Mathematics
General Mathematics
Publication Status: Published
Open Access location: http://arxiv.org/abs/1510.02315v2
Online Publication Date: 2018-09-21
Appears in Collections:Mathematics
Applied Mathematics and Mathematical Physics
Faculty of Natural Sciences



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