Confinement in nonlocal interaction equations

J.A. Carrillo; M. Di Francesco; A. Figalli; T. Laurent; D. Slepčev

doi:10.1016/j.na.2011.08.057

Confinement in nonlocal interaction equations

J.A. Carrillo, M. Di Francesco, A. Figalli, T. Laurent, D. Slepčev

Department of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

30 Citations (SciVal)

211 Downloads (Pure)

Abstract

We investigate some dynamical properties of nonlocal interaction equations. We consider sets of particles interacting pairwise via a potential W, as well as continuum descriptions of such systems. The typical potentials we consider are repulsive at short distances, but attractive at long distances. The main question we consider is whether an initially localized configuration remains localized for all times, regardless of the number of particles or their arrangement. In particular we find sufficient conditions on the potential W for the above "confinement" property to hold. We use the framework of weak measure solutions developed in Carrillo et al. (2011) [2] to provide unified treatment of both particle and continuum systems.

Original language	English
Pages (from-to)	550-558
Number of pages	9
Journal	Nonlinear Analysis: Theory Methods & Applications
Volume	75
Issue number	2
DOIs	https://doi.org/10.1016/j.na.2011.08.057
Publication status	Published - 1 Jan 2012

Access to Document

10.1016/j.na.2011.08.057

Author's accepted version
NOTICE: this is the author’s version of a work that was accepted for publication in Nonlinear Analysis: Theory, Methods & Applications. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Nonlinear Analysis: Theory, Methods & Applications, vol 75, issue 2, 2012, DOI 10.1016/j.na.2011.08.057
Accepted author manuscript, 324 KB

Cite this

@article{f9fd2d1d9944483297ee2abc5e329c6c,

title = "Confinement in nonlocal interaction equations",

abstract = "We investigate some dynamical properties of nonlocal interaction equations. We consider sets of particles interacting pairwise via a potential W, as well as continuum descriptions of such systems. The typical potentials we consider are repulsive at short distances, but attractive at long distances. The main question we consider is whether an initially localized configuration remains localized for all times, regardless of the number of particles or their arrangement. In particular we find sufficient conditions on the potential W for the above {"}confinement{"} property to hold. We use the framework of weak measure solutions developed in Carrillo et al. (2011) [2] to provide unified treatment of both particle and continuum systems. ",

author = "J.A. Carrillo and {Di Francesco}, M. and A. Figalli and T. Laurent and D. Slep{\v c}ev",

year = "2012",

month = jan,

day = "1",

doi = "10.1016/j.na.2011.08.057",

language = "English",

volume = "75",

pages = "550--558",

journal = "Nonlinear Analysis: Theory Methods & Applications",

issn = "0362-546X",

publisher = "Elsevier",

number = "2",

}

TY - JOUR

T1 - Confinement in nonlocal interaction equations

AU - Carrillo, J.A.

AU - Di Francesco, M.

AU - Figalli, A.

AU - Laurent, T.

AU - Slepčev, D.

PY - 2012/1/1

Y1 - 2012/1/1

N2 - We investigate some dynamical properties of nonlocal interaction equations. We consider sets of particles interacting pairwise via a potential W, as well as continuum descriptions of such systems. The typical potentials we consider are repulsive at short distances, but attractive at long distances. The main question we consider is whether an initially localized configuration remains localized for all times, regardless of the number of particles or their arrangement. In particular we find sufficient conditions on the potential W for the above "confinement" property to hold. We use the framework of weak measure solutions developed in Carrillo et al. (2011) [2] to provide unified treatment of both particle and continuum systems.

AB - We investigate some dynamical properties of nonlocal interaction equations. We consider sets of particles interacting pairwise via a potential W, as well as continuum descriptions of such systems. The typical potentials we consider are repulsive at short distances, but attractive at long distances. The main question we consider is whether an initially localized configuration remains localized for all times, regardless of the number of particles or their arrangement. In particular we find sufficient conditions on the potential W for the above "confinement" property to hold. We use the framework of weak measure solutions developed in Carrillo et al. (2011) [2] to provide unified treatment of both particle and continuum systems.

UR - http://www.scopus.com/inward/record.url?scp=80055013696&partnerID=8YFLogxK

UR - http://dx.doi.org/10.1016/j.na.2011.08.057

U2 - 10.1016/j.na.2011.08.057

DO - 10.1016/j.na.2011.08.057

M3 - Article

AN - SCOPUS:80055013696

SN - 0362-546X

VL - 75

SP - 550

EP - 558

JO - Nonlinear Analysis: Theory Methods & Applications

JF - Nonlinear Analysis: Theory Methods & Applications

IS - 2

ER -

Confinement in nonlocal interaction equations

Abstract

Access to Document

Other files and links

Fingerprint

Cite this