CONFINEMENT FOR REPULSIVE-ATTRACTIVE KERNELS

被引：21

作者：

Balague, Daniel ^{[1
]}

Carrillo, Jose A. ^{[2
]}

Yao, Yao ^{[3
]}

机构：

[1] N Carolina State Univ, Dept Math, Raleigh, NC 27695 USA

[2] Univ London Imperial Coll Sci Technol & Med, Dept Math, London SW7 2AZ, England

[3] Univ Wisconsin, Dept Math, Madison, WI 53706 USA

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B | 2014年 / 19卷 / 05期

基金：

英国工程与自然科学研究理事会;

关键词：

Aggregation equation; particle systems; confinement; STATIONARY STATES; GRADIENT FLOW; MODEL; AGGREGATION; EQUATIONS; STABILITY; PATTERNS; LIMIT;

D O I：

10.3934/dcdsb.2014.19.1227

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We investigate the confinement properties of solutions of the aggregation equation with repulsive-attractive potentials. We show that solutions remain compactly supported in a large fixed ball depending on the initial data and the potential. The arguments apply to the functional setting of probability measures with mildly singular repulsive-attractive potentials and to the functional setting of smooth solutions with a potential being the sum of the Newtonian repulsion at the origin and a smooth suitably growing at infinity attractive potential.

引用

页码：1227 / 1248

页数：22

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