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
CAMASSA, R
HOLM, DD
[J]. PHYSICAL REVIEW LETTERS, 1993, 71 (11) : 1661 - 1664
[2] A two-component generalization of the Camassa-Holm equation and its solutions
Chen, M
Liu, SQ
Zhang, YJ
[J]. LETTERS IN MATHEMATICAL PHYSICS, 2006, 75 (01) : 1 - 15
[3] On the cauchy problem for the periodic Camassa-Holm equation
Constantin, A
[J]. JOURNAL OF DIFFERENTIAL EQUATIONS, 1997, 141 (02) : 218 - 235
[4] Wave breaking for nonlinear nonlocal shallow water equations
Constantin, A
Escher, J
[J]. ACTA MATHEMATICA, 1998, 181 (02) : 229 - 243
[5] On the blow-up of solutions of a periodic shallow water equation
Constantin, A
[J]. JOURNAL OF NONLINEAR SCIENCE, 2000, 10 (03) : 391 - 399
[6] On an integrable two-component Camassa-Holm shallow water system
Constantin, Adrian
Ivanov, Rossen I.
[J]. PHYSICS LETTERS A, 2008, 372 (48) : 7129 - 7132
[7] The geometry of the two-component Camassa-Holm and Degasperis-Procesi equations
Escher, J.
Kohlmann, M.
Lenells, J.
[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
Guo, Zhengguang
Zhu, Mingxuan
[J]. JOURNAL OF DIFFERENTIAL EQUATIONS, 2012, 252 (03) : 2759 - 2770
[10] On Solutions to a Two-Component Generalized Camassa-Holm Equation
Guo, Zhengguang
Zhou, Yong
[J]. STUDIES IN APPLIED MATHEMATICS, 2010, 124 (03) : 307 - 322

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