HYDRODYNAMIC CUCKER-SMALE MODEL WITH NORMALIZED COMMUNICATION WEIGHTS AND TIME DELAY

被引：19

作者：

Choi, Young-Pil ^{[1
,2
]}

Haskovec, Jan ^{[3
]}

机构：

[1] Inha Univ, Dept Math, Incheon 402751, South Korea

[2] Inha Univ, Inst Appl Math, Incheon 402751, South Korea

[3] King Abdullah Univ Sci & Technol, Comp Elect & Math Sci & Engn, Thuwal 23955, Saudi Arabia

来源：

SIAM JOURNAL ON MATHEMATICAL ANALYSIS | 2019年 / 51卷 / 03期

基金：

新加坡国家研究基金会;

关键词：

Cucker-Smale model; pressureless Euler system; classical solution; time delay; asymptotic behavior; flocking;

D O I：

10.1137/17M1139151

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study a hydrodynamic Cucker-Smale-type model with time delay in communication and information processing, in which agents interact with each other through normalized communication weights. The model consists of a pressureless Euler system with time-delayed nonlocal alignment forces. We resort to its Lagrangian formulation and prove the existence of its global-in-time classical solutions. Moreover, we derive a sufficient condition for the asymptotic flocking behavior of the solutions. Finally, we show the presence of a critical phenomenon for the Eulerian system posed in the spatially one-/two-dimensional setting.

引用

页码：2660 / 2685

页数：26

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