scholarly journals Persistence properties and wave-breaking criteria for a generalized two-component rotational b-family system

2020 ◽  
Vol 40 (4) ◽  
pp. 2475-2493
Author(s):  
Meiling Yang ◽  
◽  
Yongsheng Li ◽  
Zhijun Qiao ◽  
Keyword(s):  
Wave Breaking ◽  
Family System ◽  
Persistence Properties ◽  
Two Component

Persistence Properties of the Two-Component b-Family System

2012 ◽  
Vol 12 (2) ◽  
Author(s):  
Min Zhu ◽  
Junxiang Xu
Keyword(s):  
Family System ◽  
Initial Value ◽  
Compactly Supported ◽  
Persistence Properties ◽  
Propagation Behavior ◽  
Decay Properties ◽  
Two Component ◽  
Speed Of Propagation ◽  
Infinite Speed Of Propagation ◽  
Compactly Supported Solutions

AbstractIn this paper we study the persistence properties of decay for the solutions to the two component b-family system. Using the method of characteristics, we establish that certain decay properties of the initial data persist as long as the solution exists. We also examine the propagation behavior of compactly supported solutions. We show that solutions have an infinite speed of propagation, that is, a non-trivial strong solution with compact initial value can not be compactly supported at any later time.

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

scholarly journals Wave breaking for a generalized weakly dissipative two-component Camassa–Holm system

2013 ◽  
Vol 400 (2) ◽  
pp. 406-417 ◽  
Author(s):  
Wenxia Chen ◽  
Lixin Tian ◽  
Xiaoyan Deng ◽  
Jianmei Zhang
Keyword(s):  
Wave Breaking ◽  
Two Component

Stability of blow-up solution for the two component Camassa–Holm equations

2020 ◽  
Vol 120 (3-4) ◽  
pp. 319-336
Author(s):  
Xintao Li ◽  
Shoujun Huang ◽  
Weiping Yan
Keyword(s):  
Shallow Water ◽  
Wave Breaking ◽  
Water Regime ◽  
Blow Up ◽  
Dynamical Behavior ◽  
Water Dynamics ◽  
Two Component ◽  
Breaking Mechanism ◽  
Self Similar ◽  
Shallow Water Dynamics

This paper studies the wave-breaking mechanism and dynamical behavior of solutions near the explicit self-similar singularity for the two component Camassa–Holm equations, which can be regarded as a model for shallow water dynamics and arising from the approximation of the Hamiltonian for Euler’s equation in the shallow water regime.

Wave breaking analysis for the periodic rotation-two-component Camassa–Holm system

2019 ◽  
Vol 187 ◽  
pp. 214-228
Author(s):  
Jingjing Liu ◽  
Patrizia Pucci ◽  
Qihu Zhang
Keyword(s):  
Wave Breaking ◽  
Periodic Rotation ◽  
Two Component

Wave breaking phenomenon for a modified two-component Dullin-Gottwald-Holm equation

2014 ◽  
Vol 55 (9) ◽  
pp. 093101 ◽  
Author(s):  
Panpan Zhai ◽  
Zhengguang Guo ◽  
Weiming Wang
Keyword(s):  
Wave Breaking ◽  
Holm Equation ◽  
Two Component
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