Persistence properties of the solutions to a generalized two-component Camassa–Holm shallow water system

2015 ◽  
Vol 128 ◽  
pp. 77-85 ◽  
Author(s):  
Yuan Zhu ◽  
Fengyun Fu
Keyword(s):  
Shallow Water ◽  
Water System ◽  
Persistence Properties ◽  
Two Component ◽  
Shallow Water System

scholarly journals Blow-up Phenomena and Persistence Properties of Solutions to the Two-Component DGH Equation

2013 ◽  
Vol 2013 ◽  
pp. 1-13
Author(s):  
Panpan Zhai ◽  
Zhengguang Guo ◽  
Weiming Wang
Keyword(s):  
Initial Data ◽  
Shallow Water ◽  
Finite Time ◽  
Blow Up ◽  
Sufficient Conditions ◽  
Water System ◽  
Persistence Properties ◽  
Two Component ◽  
Shallow Water System

This paper is concerned with blow-up phenomena and persistence properties for an integrable two-component Dullin-Gottwald-Holm shallow water system. We give sufficient conditions on the initial data which guarantee blow-up phenomena of solutions in finite time for both periodic and nonperiodic cases, respectively. Furthermore, the persistence properties of solutions to the system are investigated.

scholarly journals On the Global Dissipative and Multipeakon Dissipative Behavior of the Two-Component Camassa-Holm System

2014 ◽  
Vol 2014 ◽  
pp. 1-16 ◽  
Author(s):  
Yujuan Wang ◽  
Yongduan Song ◽  
Hamid Reza Karimi
Keyword(s):  
Shallow Water ◽  
Wave Breaking ◽  
Water System ◽  
Original System ◽  
Collision Time ◽  
Two Component ◽  
Shallow Water System

The global dissipative and multipeakon dissipative behavior of the two-component Camassa-Holm shallow water system after wave breaking was studied in this paper. The underlying approach is based on a skillfully defined characteristic and a set of newly introduced variables which transform the original system into a Lagrangian semilinear system. It is the transformation, together with the associated properties, that allows for the continuity of the solution beyond collision time to be established, leading to a uniquely global dissipative solution, which constructs a semigroup, and the multipeakon dissipative solution.

On the existence of global weak solutions to an integrable two-component Camassa–Holm shallow-water system

2013 ◽  
Vol 56 (3) ◽  
pp. 755-775 ◽  
Author(s):  
Chunxia Guan ◽  
Zhaoyang Yin
Keyword(s):  
Shallow Water ◽  
Weak Solutions ◽  
Burgers Equation ◽  
Water System ◽  
Global Weak Solution ◽  
Rarefaction Waves ◽  
Global Weak Solutions ◽  
Two Component ◽  
The Cauchy Problem ◽  
Shallow Water System

AbstractIn this paper, we investigate the existence of global weak solutions to an integrable two-component Camassa–Holm shallow-water system, provided the initial datau0(x)andρ0(x)have end statesu± andρ±, respectively. By perturbing the Cauchy problem of the system around rarefaction waves of the well-known Burgers equation, we obtain a global weak solution for the system under the assumptionsu− ≤ u+andρ− ≤ ρ+.

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