SELF-SIMILAR SOLUTIONS AND BLOW-UP PHENOMENA FOR A TWO-COMPONENT SHALLOW WATER SYSTEM

doi:10.1016/S0252-9602(13)60041-7

数学物理学报(英文版) ›› 2013, Vol. 33 ›› Issue (3): 821-829.doi: 10.1016/S0252-9602(13)60041-7

SELF-SIMILAR SOLUTIONS AND BLOW-UP PHENOMENA FOR A TWO-COMPONENT SHALLOW WATER SYSTEM

周寿明^1,2|穆春来²|王良展²

1. College of Mathematics Science, Chongqing Normal University, Chongqing 400047, China；
2. College of Mathematics and Statistics, Chongqing University, Chongqing 401331, China

收稿日期:2011-11-16 出版日期:2013-05-20 发布日期:2013-05-20
基金资助:
This work is supported by NSF of China (11071266), partially supported by Scholarship Award for Excellent Doctoral Student granted by Ministry of Education and partially supported by the found of Chongqing Normal University (13XLB006).

SELF-SIMILAR SOLUTIONS AND BLOW-UP PHENOMENA FOR A TWO-COMPONENT SHALLOW WATER SYSTEM

ZHOU Shou-Ming^1,2, MU Chun-Lai², WANG Liang-Zhan²

1. College of Mathematics Science, Chongqing Normal University, Chongqing 400047, China；
2. College of Mathematics and Statistics, Chongqing University, Chongqing 401331, China

Received:2011-11-16 Online:2013-05-20 Published:2013-05-20
Supported by:
This work is supported by NSF of China (11071266), partially supported by Scholarship Award for Excellent Doctoral Student granted by Ministry of Education and partially supported by the found of Chongqing Normal University (13XLB006).

摘要/Abstract

摘要：

In this article, we consider a two-component nonlinear shallow water system, which includes the famous 2-component Camassa-Holm and Degasperis-Procesi equations as special cases. The local well-posedess for this equations is established. Some sufficient conditions for blow-up of the solutions in finite time are given. Moreover, by separation method, the self-similar solutions for the nonlinear shallow water equations are obtained, and which local or global behavior can be determined by the corresponding Emden equation.

Abstract:

Key words: Self-similar solutions, blow-up phenomena, two-component shallow water sys-tem

中图分类号:

35G25

周寿明, 穆春来, 王良展. SELF-SIMILAR SOLUTIONS AND BLOW-UP PHENOMENA FOR A TWO-COMPONENT SHALLOW WATER SYSTEM[J]. 数学物理学报(英文版), 2013, 33(3): 821-829.

ZHOU Shou-Ming, MU Chun-Lai, WANG Liang-Zhan. SELF-SIMILAR SOLUTIONS AND BLOW-UP PHENOMENA FOR A TWO-COMPONENT SHALLOW WATER SYSTEM[J]. Acta mathematica scientia,Series B, 2013, 33(3): 821-829.

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SELF-SIMILAR SOLUTIONS AND BLOW-UP PHENOMENA FOR A TWO-COMPONENT SHALLOW WATER SYSTEM

SELF-SIMILAR SOLUTIONS AND BLOW-UP PHENOMENA FOR A TWO-COMPONENT SHALLOW WATER SYSTEM

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