Decay rates for a class of diffusive-dominated interaction equations

José A. Cañizo, José A. Carrillo, Maria E. Schonbek

Research output: Contribution to journalArticleResearchpeer-review

3 Citations (Scopus)

Abstract

We analyse qualitative properties of the solutions to a mean-field equation for particles interacting through a pairwise potential while diffusing by Brownian motion. Interaction and diffusion compete with each other depending on the character of the potential. We provide sufficient conditions on the relation between the interaction potential and the initial data for diffusion to be the dominant term. We give decay rates of Sobolev norms showing that asymptotically for large times the behavior is then given by the heat equation. Moreover, we show an optimal rate of convergence in the L1-norm towards the fundamental solution of the heat equation. © 2011 Elsevier Inc.
Original languageEnglish
Pages (from-to)541-557
JournalJournal of Mathematical Analysis and Applications
Volume389
Issue number1
DOIs
Publication statusPublished - 1 May 2012

Keywords

  • Aggregation
  • Asymptotic behavior
  • Diffusion
  • Entropy methods

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