Self-similar solutions and blow-up phenomena for a two-component shallow water system

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• 作者：Shouming ZHOU^a ; ^b ; ^{zhoushouming76@163.com} ; Chunlai MU^b ; Liangchen WANG^b
• 关键词：Self-similar solutions ; blow-up phenomena ; two-component shallow water system
• 刊名：Acta Mathematica Scientia
• 出版年：2013
• 出版时间：May, 2013
• 年：2013
• 卷：33
• 期：3
• 页码：821-829
• 全文大小：307 K

文摘

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.