Decay rates for a class of diffusive-dominated interaction equations

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

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)


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.
Original languageEnglish
Pages (from-to)541-557
Number of pages17
JournalJournal of Mathematical Analysis and Applications
Issue number1
Publication statusPublished - 1 May 2012


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