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Blow up, global existence, and infinite propagation speed for the weakly dissipative Camassa-Holm equation. (English) Zbl 1153.81368
Summary: In this paper, we consider the weakly dissipative Camassa-Holm equation. First, we try to improve other authors’ results and get some new criterion on blow up, then discuss the global existence of the solution. Finally, we intend to establish sufficient conditions on the propagation speed for the weakly dissipative Camassa-Holm equation.

MSC:
35Q53 KdV equations (Korteweg-de Vries equations)
35B40 Asymptotic behavior of solutions to PDEs
35B44 Blow-up in context of PDEs
76B15 Water waves, gravity waves; dispersion and scattering, nonlinear interaction
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