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**On the Cauchy problem for the \(b\)-family equations with a strong dispersive term.**
*(English)*
Zbl 1228.35206

Summary: We consider \(b\)-family equations with a strong dispersive term. First, we present a criterion on blow-up. Then global existence and persistence property of the solution are also established. Finally, we discuss infinite propagation speed of this equation.

### MSC:

35Q53 | KdV equations (Korteweg-de Vries equations) |

35B44 | Blow-up in context of PDEs |

35A01 | Existence problems for PDEs: global existence, local existence, non-existence |

### Keywords:

\(b\)-family equations
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\textit{X. Liu} et al., J. Appl. Math. 2011, Article ID 513467, 15 p. (2011; Zbl 1228.35206)

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### References:

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