Decay rates for a class of diffusive-dominated interaction equations

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:389

Article

Canizo, Jose A.¹  Carrillo, Jose A.¹  Schonbek, Maria E.² 

[1] Univ Autonoma Barcelona, Dept Matemat, E-08193 Bellaterra, Spain

[2] UC Santa Cruz, Dept Math, Santa Cruz, CA 95064 USA

关键词: Aggregation;    Diffusion;    Asymptotic behavior;    Entropy methods;   

DOI  :  10.1016/j.jmaa.2011.12.006

来源: Elsevier

【 摘 要 】

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 L-1-norm towards the fundamental solution of the heat equation. (C) 2011 Elsevier Inc. All rights reserved.

【 授权许可】

Free