Explicit equilibrium solutions for the aggregation equation with power-law potentials

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Title: Explicit equilibrium solutions for the aggregation equation with power-law potentials
Author(s): Carrillo, JA
Huang, Y
Item 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.
Publication Date: 1-Nov-2016
Date of Acceptance: 1-Nov-2016
URI: http://hdl.handle.net/10044/1/43926
DOI: http://dx.doi.org/10.3934/krm.2017007
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/Funder: The Royal Society
Funder's Grant Number: WM120001
Keywords: 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
Embargo Date: 2017-11-01
Appears in Collections:Mathematics
Applied Mathematics and Mathematical Physics
Faculty of Natural Sciences



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