Hydrodynamic limits for kinetic flocking models of Cucker-Smale type

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Title: Hydrodynamic limits for kinetic flocking models of Cucker-Smale type
Authors: Aceves Sanchez, P
Bostan, M
Carrillo de la Plata, JA
Degond, P
Item Type: Journal Article
Abstract: We analyse the asymptotic behavior for kinetic models describing the collective behavior of animal populations. We focus on models for self-propelled individuals, whose velocity relaxes toward the mean orientation of the neighbors. The self-propelling and friction forces together with the alignment and the noise are interpreted as a collision/interaction mechanism acting with equal strength. We show that the set of generalized collision invariants, introduced in [39], is equivalent in our setting to the more classical notion of collision invariants, i.e., the kernel of a suitably linearized collision operator. After identifying these collision invariants, we derive the fluid model, by appealing to the balances for the particle concentration and orientation. We investigate the main properties of the macroscopic model for a general potential with radial symmetry.
Issue Date: 28-Aug-2019
Date of Acceptance: 5-Jun-2019
URI: http://hdl.handle.net/10044/1/70263
DOI: https://dx.doi.org/10.3934/mbe.2019396
ISSN: 1547-1063
Publisher: American Institute of Mathematical Sciences
Start Page: 7883
End Page: 7910
Journal / Book Title: Mathematical Biosciences and Engineering
Volume: 16
Issue: 6
Copyright Statement: © 2019 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
Sponsor/Funder: The Royal Society
Engineering & Physical Science Research Council (EPSRC)
Engineering & Physical Science Research Council (EPSRC)
Engineering & Physical Science Research Council (EPSRC)
Funder's Grant Number: WM130048
Keywords: 0102 Applied Mathematics
0903 Biomedical Engineering
0904 Chemical Engineering
Publication Status: Published
Online Publication Date: 2019-08-28
Appears in Collections:Mathematics
Applied Mathematics and Mathematical Physics
Faculty of Natural Sciences

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