## Abstract and Applied Analysis

### The Local Strong and Weak Solutions for a Generalized Novikov Equation

#### 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 $C([0,T),{H}^{s}(R))\cap {C}^{1}([0,T),{H}^{s-1}(R))$ with $s>(3/2)$. The existence of weak solutions for the equation in lower-order Sobolev space ${H}^{s}(R)$ with $1\le s\le (3/2)$ is acquired.

#### Article information

Source
Abstr. Appl. Anal., Volume 2012, Special Issue (2012), Article ID 158126, 14 pages.

Dates
First available in Project Euclid: 4 April 2013

https://projecteuclid.org/euclid.aaa/1365099919

Digital Object Identifier
doi:10.1155/2012/158126

Mathematical Reviews number (MathSciNet)
MR2903806

Zentralblatt MATH identifier
1243.35044

#### Citation

Wu, Meng; Zhong, Yue. The Local Strong and Weak Solutions for a Generalized Novikov Equation. Abstr. Appl. Anal. 2012, Special Issue (2012), Article ID 158126, 14 pages. doi:10.1155/2012/158126. https://projecteuclid.org/euclid.aaa/1365099919

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