Asymptotic Behavior of Gradient Flows Driven by Nonlocal Power Repulsion and Attraction Potentials in One Dimension

We study the long-time behavior of the Wasserstein gradient flow for an energy functional consisting of two components: particles are attracted to a fixed profile $\omega$ by means of an interaction kernel $\psi_a(z)=|z|q_a}$, and they repel each other by means of another kernel $\psi_r(z)=|z|q_r}$....

Full description

Saved in:
Bibliographic Details
Published in:SIAM journal on mathematical analysis 2014-01, Vol.46 (6), p.3814-3837
Main Authors: Di Francesco, Marco, Fornasier, Massimo, Hütter, Jan-Christian, Matthes, Daniel
Format: Article
Language:English
Subjects:
Attraction
Distribution functions
Gradient flow
Initial conditions
Inverse
Kernels
Mathematical analysis
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We study the long-time behavior of the Wasserstein gradient flow for an energy functional consisting of two components: particles are attracted to a fixed profile $\omega$ by means of an interaction kernel $\psi_a(z)=|z|q_a}$, and they repel each other by means of another kernel $\psi_r(z)=|z|q_r}$. We focus on the case of one space dimension and assume that $1\le q_r\le q_a\le 2$. Our main result is that the flow converges to an equilibrium if either $q_r
ISSN:0036-1410
1095-7154
DOI:10.1137/140951497