scholarly journals Wave breaking and infinite propagation speed for a modified two-component Camassa-Holm system with κ≠0

2014 ◽  
Vol 2014 (1) ◽  
pp. 125 ◽  
Author(s):  
Wujun Lv ◽  
Ahmed Alsaedi ◽  
Tasawar Hayat ◽  
Yong Zhou
Keyword(s):  
Wave Breaking ◽  
Propagation Speed ◽  
Two Component ◽  
Infinite Propagation Speed

scholarly journals The dynamic properties of solutions for a nonlinear shallow water equation

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Yeqin Su ◽  
Shaoyong Lai ◽  
Sen Ming
Keyword(s):  
Cauchy Problem ◽  
Global Existence ◽  
Shallow Water ◽  
Wave Breaking ◽  
Dynamic Properties ◽  
Shallow Water Equation ◽  
Propagation Speed ◽  
Well Posedness ◽  
The Cauchy Problem ◽  
Infinite Propagation Speed

Abstract The local well-posedness for the Cauchy problem of a nonlinear shallow water equation is established. The wave-breaking mechanisms, global existence, and infinite propagation speed of solutions to the equation are derived under certain assumptions. In addition, the effects of coefficients λ, β, a, b, and index k in the equation are illustrated.

scholarly journals Wave Breaking and Propagation Speed for a Class of One-Dimensional Shallow Water Equations

2011 ◽  
Vol 2011 ◽  
pp. 1-15 ◽  
Author(s):  
Zaihong Jiang ◽  
Sevdzhan Hakkaev
Keyword(s):  
Initial Data ◽  
Shallow Water ◽  
Shallow Water Equations ◽  
Finite Time ◽  
Wave Breaking ◽  
Blow Up ◽  
Propagation Speed ◽  
One Dimensional ◽  
General Family ◽  
Infinite Propagation Speed

We investigate a more general family of one-dimensional shallow water equations. Analogous to the Camassa-Holm equation, these new equations admit blow-up phenomenon and infinite propagation speed. First, we establish blow-up results for this family of equations under various classes of initial data. It turns out that it is the shape instead of the size and smoothness of the initial data which influences breakdown in finite time. Then, infinite propagation speed for the shallow water equations is proved in the following sense: the corresponding solutionu(t,x)with compactly supported initial datumu0(x)does not have compactx-support any longer in its lifespan.

scholarly journals Blow-Up Analysis for the Periodic Two-Component μ-Hunter-Saxton System

2018 ◽  
Vol 2018 ◽  
pp. 1-11
Author(s):  
Yunxi Guo ◽  
Tingjian Xiong
Keyword(s):  
Transport Equation ◽  
Wave Breaking ◽  
Blow Up ◽  
Sufficient Conditions ◽  
Blow Up Analysis ◽  
Classic Method ◽  
Two Component ◽  
Localization Analysis ◽  
Spatially Periodic ◽  
Periodic Setting

The two-component μ-Hunter-Saxton system is considered in the spatially periodic setting. Firstly, a wave-breaking criterion is derived by employing the localization analysis of the transport equation theory. Secondly, several sufficient conditions of the blow-up solutions are established by using the classic method. The results obtained in this paper are new and different from those in previous works.

On the wave-breaking phenomena for the two-component Dullin-Gottwald-Holm system

2012 ◽  
Vol 86 (3) ◽  
pp. 810-834 ◽  
Author(s):  
Fei Guo ◽  
Hongjun Gao ◽  
Yue Liu
Keyword(s):  
Wave Breaking ◽  
Two Component
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