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

被引：1
|
作者：
Wang, Yujuan [1 ]
Song, Yongduan [1 ]
Karimi, Hamid Reza [2 ]
机构：
[1] Chongqing Univ, Sch Automat, Chongqing 400044, Peoples R China
[2] Univ Agder, Fac Sci & Engn, Dept Engn, N-4898 Grimstad, Norway
来源：
ABSTRACT AND APPLIED ANALYSIS | 2014年
基金：
中国国家自然科学基金;
关键词：
SHALLOW-WATER EQUATION; BLOW-UP PHENOMENA; CONSERVATIVE SOLUTIONS; WAVE-BREAKING; EXISTENCE;
D O I：
10.1155/2014/348695
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
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.
引用
收藏
页数：16
相关论文
共 50 条
  • [1] Global Dissipative Multipeakon Solutions of the Camassa-Holm Equation
    Holden, H.
    Raynaud, X.
    [J]. COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 2008, 33 (11) : 2040 - 2063
  • [2] Dissipative solutions for the modified two-component Camassa-Holm system
    Wang, Yujuan
    Song, Yongduan
    [J]. NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS, 2014, 21 (03): : 339 - 360
  • [3] GLOBAL DISSIPATIVE SOLUTIONS FOR THE TWO-COMPONENT CAMASSA-HOLM SHALLOW WATER SYSTEM
    Wang, Yujuan
    Song, Yongduan
    [J]. ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS, 2015,
  • [4] Global dissipative solutions of a modified two-component Camassa-Holm shallow water system
    Tan, Wenke
    Yin, Zhaoyang
    [J]. JOURNAL OF MATHEMATICAL PHYSICS, 2011, 52 (03)
  • [5] Global conservative and multipeakon conservative solutions for the two-component Camassa-Holm system
    Yujuan Wang
    Yongduan Song
    [J]. Boundary Value Problems, 2013
  • [6] Global conservative and multipeakon conservative solutions for the two-component Camassa-Holm system
    Wang, Yujuan
    Song, Yongduan
    [J]. BOUNDARY VALUE PROBLEMS, 2013,
  • [7] Dissipative prolongations of the multipeakon solutions to the Camassa-Holm equation
    Krynski, Wojciech
    [J]. JOURNAL OF DIFFERENTIAL EQUATIONS, 2019, 266 (04) : 1832 - 1850
  • [8] Symmetries and multipeakon solutions for the modified two-component Camassa-Holm system
    Grunert, Katrin
    Raynaud, Xavier
    [J]. NON-LINEAR PARTIAL DIFFERENTIAL EQUATIONS, MATHEMATICAL PHYSICS, AND STOCHASTIC ANALYSIS: THE HELGE HOLDEN ANNIVERSARY VOLME, 2018, : 227 - 260
  • [9] Wave breaking for a generalized weakly dissipative two-component Camassa-Holm system
    Chen, Wenxia
    Tian, Lixin
    Deng, Xiaoyan
    Zhang, Jianmei
    [J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2013, 400 (02) : 406 - 417
  • [10] Global dissipative solutions of the two-component Camassa-Holm system for initial data with nonvanishing asymptotics
    Grunert, Katrin
    Holden, Helge
    Raynaud, Xavier
    [J]. NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, 2014, 17 : 203 - 244
12345