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.


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
Full Text: DOI


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