On blow-up of solutions to the two-component π-Camassa-Holm system

被引：2

作者：

Ma, Caochuan ^{[1
]}

Alsaedi, Ahmed ^{[2
]}

Hayat, Tasawar ^{[2
,3
,4
]}

Zhou, Yong ^{[2
,5
]}

机构：

[1] Tianshui Normal Univ, Sch Math & Stat, Tianshui 741001, Peoples R China

[2] King Abdulaziz Univ, Fac Sci, Res Grp, NAAM, Jeddah 21589, Saudi Arabia

[3] Quaid I Azam Univ, Dept Math, Islamabad 45320, Pakistan

[4] Quaid I Azam Univ, Dept Math, Islamabad 44000, Pakistan

[5] Shanghai Univ Finance & Econ, Sch Math, Shanghai 200433, Peoples R China

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2015年 / 426卷 / 02期

关键词：

pi-Camassa-Holm system; Geodesic flow; Blow-up; Blow-up rate; SHALLOW-WATER EQUATION; WAVE BREAKING; SOLITONS; GEOMETRY;

D O I：

10.1016/j.jmaa.2015.02.010

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We investigate Cauchy problem of the two-component pi-Camassa-Holm system which arises from geodesic flow on a semidirect product Lie group of the circle. The precise blow-up scenarios of strong solutions are derived for the system. Then, several criteria to guarantee blow-up of strong solutions are presented. Finally, the exact blow-up rate is determined. (C) 2015 Elsevier Inc. All rights reserved.

引用

页码：1026 / 1039

页数：14

共 22 条

[1] AN INTEGRABLE SHALLOW-WATER EQUATION WITH PEAKED SOLITONS [J].

CAMASSA, R ;

HOLM, DD .

PHYSICAL REVIEW LETTERS, 1993, 71 (11) :1661-1664

[2] A two-component generalization of the Camassa-Holm equation and its solutions [J].

Chen, M ;

Liu, SQ ;

Zhang, YJ .

LETTERS IN MATHEMATICAL PHYSICS, 2006, 75 (01) :1-15

[3] On the cauchy problem for the periodic Camassa-Holm equation [J].

Constantin, A .

JOURNAL OF DIFFERENTIAL EQUATIONS, 1997, 141 (02) :218-235

[4] Wave breaking for nonlinear nonlocal shallow water equations [J].

Constantin, A ;

Escher, J .

ACTA MATHEMATICA, 1998, 181 (02) :229-243

[5] On the blow-up of solutions of a periodic shallow water equation [J].

Constantin, A .

JOURNAL OF NONLINEAR SCIENCE, 2000, 10 (03) :391-399

[6] On an integrable two-component Camassa-Holm shallow water system [J].

Constantin, Adrian ;

Ivanov, Rossen I. .

PHYSICS LETTERS A, 2008, 372 (48) :7129-7132

[7] The geometry of the two-component Camassa-Holm and Degasperis-Procesi equations [J].

Escher, J. ;

Kohlmann, M. ;

Lenells, J. .

JOURNAL OF GEOMETRY AND PHYSICS, 2011, 61 (02) :436-452

[8]

Escher J, 2007, DISCRETE CONT DYN-A, V19, P493

[9] Wave breaking for a modified two-component Camassa-Holm system [J].

Guo, Zhengguang ;

Zhu, Mingxuan .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2012, 252 (03) :2759-2770

[10] On Solutions to a Two-Component Generalized Camassa-Holm Equation [J].

Guo, Zhengguang ;

Zhou, Yong .

STUDIES IN APPLIED MATHEMATICS, 2010, 124 (03) :307-322

← 1 2 3 →