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

Part of: General higher-order equations and systems Hyperbolic equations and systems

Published online by Cambridge University Press:  28 June 2013

Chunxia Guan  and
Zhaoyang Yin
Chunxia Guan
Affiliation:
Institut Franco-Chinois de L'Energie Nucléaire, Sun Yat-sen University, 510275 Guangzhou, People's Republic of China (guanchunxia123@163.com)
Zhaoyang Yin
Affiliation:
Department of Mathematics, Sun Yat-sen University, 510275 Guangzhou, People's Republic of China (mcsyzy@mail.sysu.edu.cn)
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Abstract

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In this paper, we investigate the existence of global weak solutions to an integrable two-component Camassa–Holm shallow-water system, provided the initial data u0(x) and ρ0(x) have end states u± and ρ±, 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 assumptions u− ≤ u+ and ρ− ≤ ρ+.

Keywords

integrable two-component Camassa–Holm shallow-water systemrarefaction waveglobal weak solutions

MSC classification

Secondary: 35G25: Initial value problems for nonlinear higher-order equations 35L05: Wave equation
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 56 , Issue 3 , October 2013 , pp. 755 - 775
Copyright
Copyright © Edinburgh Mathematical Society 2013 

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