Explicit equilibrium solutions for the aggregation equation with power-law potentials
File(s)
Accepted version
Author(s)
Carrillo, JA
Huang, Y
Type
Journal Article
Abstract
Despite their wide presence in various models in the study of collective behaviors, explicit swarming patterns are difficult to obtain. In this paper, special stationary solutions of the aggregation equation with power-law kernels are constructed by inverting Fredholm integral operators or by employing certain integral identities. These solutions are expected to be the global energy stable equilibria and to characterize the generic behaviors of stationary solutions for more general interactions.
Date Issued
2016-11-01
Date Acceptance
2016-11-01
Citation
Kinetic and Related Models, 2016, 10 (1), pp.171-192
ISSN
1937-5093
Publisher
American Institute of Mathematical Sciences (AIMS)
Start Page
171
End Page
192
Journal / Book Title
Kinetic and Related Models
Volume
10
Issue
1
Copyright Statement
© 2016 American Institute for Mathematical Sciences. This is a pre-copy-editing, author-produced PDF of an article accepted for publication in Kinetic and Related Models following peer review. The definitive publisher-authenticated version is available online at: http://dx.doi.org/10.3934/krm.2017007
Sponsor
The Royal Society
Identifier
http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000390102700008&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=1ba7043ffcc86c417c072aa74d649202
Grant Number
WM120001
Subjects
Science & Technology
Physical Sciences
Mathematics, Applied
Mathematics
Fredholm integral equations
stationary solutions
NONLOCAL INTERACTION EQUATIONS
INTERACTION ENERGY
STATIONARY STATES
LOCAL MINIMIZERS
SWARMING MODELS
FLOCK SOLUTIONS
STABILITY
PARTICLE
DYNAMICS
SYSTEMS
Applied Mathematics
Publication Status
Published