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Mathematical Problems in Engineering
Volume 2014 (2014), Article ID 162472, 8 pages
http://dx.doi.org/10.1155/2014/162472
Research Article

Several Dynamical Properties for a Nonlinear Shallow Water Equation

Department of Mathematics, Southwestern University of Finance and Economics, Chengdu 611130, China

Received 18 April 2014; Accepted 8 May 2014; Published 22 May 2014

Academic Editor: Gongnan Xie

Copyright © 2014 Ls Yong and Haibo Yan. 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

A nonlinear third order dispersive shallow water equation including the Degasperis-Procesi model is investigated. The existence of weak solutions for the equation is proved in the space under certain assumptions. The Oleinik type estimate and   ( is a natural number) estimate for the solution are obtained.