On a two-component Degasperis–Procesi shallow water system

2010 ◽  
Vol 11 (5) ◽  
pp. 4164-4173 ◽  
Author(s):  
Liangbing Jin ◽  
Zhengguang Guo
Keyword(s):  
Shallow Water ◽  
Water System ◽  
Two Component ◽  
Shallow Water System

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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