Abstract and Applied Analysis
Volume 2012 (2012), Article ID 158126, 14 pages
http://dx.doi.org/10.1155/2012/158126
Research Article

The Local Strong and Weak Solutions for a Generalized Novikov Equation

Meng Wu and Yue Zhong

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

Received 8 December 2011; Accepted 13 January 2012

Academic Editor: Shaoyong Lai

Copyright © 2012 Meng Wu and Yue Zhong. 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 Kato theorem for abstract differential equations is applied to establish the local well-posedness of the strong solution for a nonlinear generalized Novikov equation in space 𝐶 ( [ 0 , 𝑇 ) , 𝐻 𝑠 ( 𝑅 ) ) ∩ 𝐶 1 ( [ 0 , 𝑇 ) , 𝐻 𝑠 − 1 ( 𝑅 ) ) with 𝑠 > ( 3 / 2 ) . The existence of weak solutions for the equation in lower-order Sobolev space 𝐻 𝑠 ( 𝑅 ) with 1 ≤ 𝑠 ≤ ( 3 / 2 ) is acquired.