Abstract and Applied Analysis
- Abstr. Appl. Anal.
- Volume 2012, Special Issue (2012), Article ID 872187, 15 pages.
The Well-Posedness of Solutions for a Generalized Shallow Water Wave Equation
A nonlinear partial differential equation containing the famous Camassa-Holm and Degasperis-Procesi equations as special cases is investigated. The Kato theorem for abstract differential equations is applied to establish the local well-posedness of solutions for the equation in the Sobolev space with . Although the -norm of the solutions to the nonlinear model does not remain constant, the existence of its weak solutions in the lower-order Sobolev space with is proved under the assumptions and .
Abstr. Appl. Anal., Volume 2012, Special Issue (2012), Article ID 872187, 15 pages.
First available in Project Euclid: 4 April 2013
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Lai, Shaoyong; Wang, Aiyin. The Well-Posedness of Solutions for a Generalized Shallow Water Wave Equation. Abstr. Appl. Anal. 2012, Special Issue (2012), Article ID 872187, 15 pages. doi:10.1155/2012/872187. https://projecteuclid.org/euclid.aaa/1365099943