Abstract and Applied Analysis
Volume 2013 (2013), Article ID 619068, 5 pages
http://dx.doi.org/10.1155/2013/619068
Research Article

The Local Strong Solutions and Global Weak Solutions for a Nonlinear Equation

Meng Wu

Department of Mathematics, Southwestern University of Finance and Economics, Chengdu 610074, China

Received 31 March 2013; Accepted 26 April 2013

Academic Editor: Shaoyong Lai

Copyright © 2013 Meng Wu. 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 existence and uniqueness of local strong solutions for a nonlinear equation are investigated in the Sobolev space provided that the initial value lies in with . Meanwhile, we prove the existence of global weak solutions in for the equation.