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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
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+.
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- 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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