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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 851476, 7 pages
http://dx.doi.org/10.1155/2013/851476
Research Article

On the Cauchy Problem for a Class of Weakly Dissipative One-Dimensional Shallow Water Equations

Department of Mathematics, Zhejiang Normal University, Jinhua 321004, China

Received 21 June 2013; Accepted 22 August 2013

Academic Editor: Sining Zheng

Copyright © 2013 Jingjing Xu and Zaihong Jiang. 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

We investigate a more general family of one-dimensional shallow water equations with a weakly dissipative term. First, we establish blow-up criteria for this family of equations. Then, global existence of the solution is also proved. Finally, we discuss the infinite propagation speed of this family of equations.