Journal of Applied Mathematics
Volume 2011 (2011), Article ID 513467, 15 pages
http://dx.doi.org/10.1155/2011/513467
Research Article

On the Cauchy Problem for the b-Family Equations with a Strong Dispersive Term

Xuefei Liu,1 Mingxuan Zhu,2 and Zaihong Jiang2

1College of Mathematics and Computer Science, Chongqing Three Gorges University, Wanzhou 404000, Chongqing, China
2Department of Mathematics, Zhejiang Normal University, Jinhua 321004, Zhejiang, China

Received 2 June 2011; Accepted 23 August 2011

Academic Editor: J. Biazar

Copyright © 2011 Xuefei Liu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

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.