Threshold for shock formation in the hyperbolic Keller-Segel model

被引：7
作者：
Lee, Yongki [1 ]
Liu, Hailiang [2 ]
机构：
[1] Univ Calif Riverside, Dept Math, Riverside, CA 92521 USA
[2] Iowa State Univ, Dept Math, Ames, IA 50010 USA
来源：
APPLIED MATHEMATICS LETTERS | 2015年 / 50卷
基金：
美国国家科学基金会;
关键词：
Non local conservation law; Keller-Segel model; Shock formation; Critical threshold; Traffic flow; TRAFFIC FLOW; CHEMOTAXIS;
D O I：
10.1016/j.aml.2015.06.001
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We identify a sub-threshold for finite time shock formation in solutions to the onedimensional hyperbolic Keller-Segel model. The main result states that under some assumptions on the initial potential, if the slope of the initial density is above a threshold at even one location, the solution must become discontinuous in finite time. (C) 2015 Elsevier Ltd. All rights reserved.
引用
收藏
页码：56 / 63
页数：8
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