Acta mathematica scientia, Series B >
SELF-SIMILAR SOLUTIONS AND BLOW-UP PHENOMENA FOR A TWO-COMPONENT SHALLOW WATER SYSTEM
Received date: 2011-11-16
Online 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).
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.
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 . DOI: 10.1016/S0252-9602(13)60041-7
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