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

共 50 条

[31] On solutions of the two-component Camassa-Holm system
Wu, Chao-Zhong
JOURNAL OF MATHEMATICAL PHYSICS, 2006, 47 (08)
[32] Blow-up phenomena and local well-posedness for a generalized Camassa-Holm equation with cubic nonlinearity
Li, Min
Yin, Zhaoyang
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2017, 151 : 208 - 226
[33] Blow-up and local weak solution for a modified two-component Camassa-Holm equations
Tian, Lixin
Zhu, Minyi
BOUNDARY VALUE PROBLEMS, 2012,
[34] Blow-up and local weak solution for a modified two-component Camassa-Holm equations
Lixin Tian
Minyi Zhu
Boundary Value Problems, 2012
[35] Well-posedness and blow-up for a modified two-component Camassa-Holm equation
Yu, Shengqi
APPLICABLE ANALYSIS, 2012, 91 (07) : 1321 - 1337
[36] On an integrable two-component Camassa-Holm shallow water system
Constantin, Adrian
Ivanov, Rossen I.
PHYSICS LETTERS A, 2008, 372 (48) : 7129 - 7132
[37] Well-posedness, global existence and blow-up phenomena for an integrable multi-component Camassa-Holm system
Zhang, Zeng
Yin, Zhaoyang
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2016, 142 : 112 - 133
[38] Local-in-Space Blow-up for a Weakly Dissipative Generalized Two-Component Camassa-Holm System
Cheng, Wenguang
JOURNAL OF MATHEMATICAL FLUID MECHANICS, 2022, 24 (01)
[39] Local-in-space blow-up and symmetric waves for a generalized two-component Camassa-Holm system
Yang, Shaojie
Xu, Tianzhou
APPLIED MATHEMATICS AND COMPUTATION, 2019, 347 : 514 - 521
[40] Local well-posedness and blow-up phenomenon for a generalization two-component Camassa-Holm system
Chen, Yuhui
Huang, Jingchi
Luo, Wei
Yu, Fang
JOURNAL OF EVOLUTION EQUATIONS, 2019, 19 (04) : 935 - 963

← 1 2 3 4 5 →