Nonlocal interactions by repulsive–attractive potentials: Radial ins/stability

D. Balagué, J.A. Carrillo, T. Laurent, G. Raoul

Research output: Contribution to journalArticlepeer-review

60 Scopus citations

Abstract

We investigate nonlocal interaction equations with repulsive-attractive radial potentials. Such equations describe the evolution of a continuum density of particles in which they repulse (resp. attract) each other in the short (resp. long) range. We prove that under some conditions on the potential, radially symmetric solutions converge exponentially fast in some transport distance toward a spherical shell stationary state. Otherwise we prove that it is not possible for a radially symmetric solution to converge weakly toward the spherical shell stationary state. We also investigate under which condition it is possible for a non-radially symmetric solution to converge toward a singular stationary state supported on a general hypersurface. Finally we provide a detailed analysis of the specific case of the repulsive-attractive power law potential as well as numerical results. © 2012 Elsevier B.V. All rights reserved.
Original languageEnglish (US)
Pages (from-to)5-25
Number of pages21
JournalPhysica D: Nonlinear Phenomena
Volume260
DOIs
StatePublished - Oct 2013
Externally publishedYes

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Condensed Matter Physics

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