Blow-up phenomena for an integrable two-component Camassa-Holm system with cubic nonlinearity and peakon solutions

被引：16

作者：

Yan, Kai ^{[1
]}

Qiao, Zhijun ^{[2
]}

Zhang, Yufeng ^{[3
]}

机构：

[1] Huazhong Univ Sci & Technol, Sch Math & Stat, Wuhan 430074, Hubei, Peoples R China

[2] Univ Texas Pan Amer, Dept Math, Edinburg, TX 78541 USA

[3] China Univ Min & Technol, Coll Sci, Xuzhou 221116, Jiangsu, Peoples R China

来源：

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

基金：

中国国家自然科学基金;

关键词：

Two-component Camassa-Holm system; Cubic nonlinearity; Fokas-Olver-Rosenau-Qiao equation; Peakons; Well-posedness; Blow-up; SHALLOW-WATER EQUATION; GLOBAL EXISTENCE; WELL-POSEDNESS; WAVE-BREAKING; WEAK SOLUTIONS; CAUCHY-PROBLEM;

D O I：

10.1016/j.jde.2015.08.004

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

This paper is devoted to an integrable two-component Camassa-Holm system with cubic nonlinearity, which includes the cubic Camassa Holm equation (also called the Fokas-Olver-Rosenau-Qiao equation) as a special case. The one peaked solitons (peakons) and two peakon solutions are described in an explicit formula. Then, the local well-posedness for the Cauchy problem of the system is studied. Moreover, we target at the precise blow-up scenario for strong solutions to the system, and establish a new blow-up result with respect to the initial data. (C) 2015 Elsevier Inc. All rights reserved.

引用

页码：6644 / 6671

页数：28

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