scholarly journals Global weak solutions for a two-component Camassa–Holm shallow water system

2011 ◽  
Vol 260 (4) ◽  
pp. 1132-1154 ◽  
Author(s):  
Chunxia Guan ◽  
Zhaoyang Yin
Keyword(s):  
Shallow Water ◽  
Weak Solutions ◽  
Water System ◽  
Global Weak Solutions ◽  
Two Component ◽  
Shallow Water System

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+.

scholarly journals AN ENERGETICALLY CONSISTENT VISCOUS SEDIMENTATION MODEL

2009 ◽  
Vol 19 (03) ◽  
pp. 477-499 ◽  
Author(s):  
JEAN DE DIEU ZABSONRÉ ◽  
CARINE LUCAS ◽  
ENRIQUE FERNÁNDEZ-NIETO
Keyword(s):  
Shallow Water ◽  
Weak Solutions ◽  
Numerical Experiments ◽  
Water System ◽  
Two Dimensional ◽  
Sedimentation Model ◽  
Shallow Water System ◽  
Periodic Domains ◽  
The Stability

In this paper we consider a two-dimensional viscous sedimentation model which is a viscous Shallow–Water system coupled with a diffusive equation that describes the evolution of the bottom. For this model, we prove the stability of weak solutions for periodic domains and give some numerical experiments. We also discuss around various discharge quantity choices.

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.

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