In this paper, 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.
"On the Cauchy Problem for the b-Family Equations with a Strong Dispersive Term." J. Appl. Math. 2011 1 - 15, 2011. https://doi.org/10.1155/2011/513467