Self-similar solutions and blow-up phenomena for a two-component shallow water system |
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| Authors: | Shouming ZHOU Chunlai MU Liangchen WANG |
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| Institution: | 1. College of Mathematics Science, Chongqing Normal University, Chongqing 400047, China;2. College of Mathematics and Statistics, Chongqing University, Chongqing 401331, China |
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| Abstract: | 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. |
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| Keywords: | Self-similar solutions blow-up phenomena two-component shallow water system |
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