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

Published online by Cambridge University Press:  28 June 2013

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)

Abstract

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+.

Type
Research Article
Copyright
Copyright © Edinburgh Mathematical Society 2013 

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