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Abstract and Applied Analysis
Volume 2014, Article ID 781813, 6 pages
http://dx.doi.org/10.1155/2014/781813
Research Article

The Local Stability of Solutions for a Nonlinear Equation

Haibo Yan1,2 and Ls Yong1

1Department of Applied Mathematics, Southwestern University of Finance and Economics, Chengdu 610074, China
2Department of Mathematics, Xinjiang University of Finance and Economics, Urumqi 830012, China

Received 15 January 2014; Accepted 19 March 2014; Published 17 April 2014

Academic Editor: Yonghong Wu

Copyright © 2014 Haibo Yan and Ls Yong. 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

The approach of Kruzkov’s device of doubling the variables is applied to establish the local stability of strong solutions for a nonlinear partial differential equation in the space by assuming that the initial value only lies in the space .