First-order aggregation models and zero inertia limits

被引：21

作者：

Fetecau, R. C. ^{[1
]}

Sun, W. ^{[1
]}

机构：

[1] Simon Fraser Univ, Dept Math, Burnaby, BC V5A 1S6, Canada

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2015年 / 259卷 / 11期

基金：

加拿大自然科学与工程研究理事会;

关键词：

Aggregation models; Kinetic equations; Macroscopic limit; Measure solutions; Mass transportation; Particle methods; NONLOCAL INTERACTION EQUATIONS; CELL-BASED MODELS; BLOW-UP; DYNAMICS; PARTICLE; SYSTEMS; SWARM;

D O I：

10.1016/j.jde.2015.08.018

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We consider a first-order aggregation model in both discrete and continuum formulations and show rigorously how it can be obtained as zero inertia limits of second-order models. In the continuum case the procedure consists in a macroscopic limit, enabling the passage from a kinetic model for aggregation to an evolution equation for the macroscopic density. We work within the general space of measure solutions and use mass transportation ideas and the characteristic method as essential tools in the analysis. (C) 2015 Elsevier Inc. All rights reserved.

引用

页码：6774 / 6802

页数：29

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