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2012 The Well-Posedness of Solutions for a Generalized Shallow Water Wave Equation
Shaoyong Lai, Aiyin Wang
Abstr. Appl. Anal. 2012(SI11): 1-15 (2012). DOI: 10.1155/2012/872187

Abstract

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 Hs(R) with s>3/2. Although the H1-norm of the solutions to the nonlinear model does not remain constant, the existence of its weak solutions in the lower-order Sobolev space Hs with 1s3/2 is proved under the assumptions u0Hs and u0xL<.

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Shaoyong Lai. Aiyin Wang. "The Well-Posedness of Solutions for a Generalized Shallow Water Wave Equation." Abstr. Appl. Anal. 2012 (SI11) 1 - 15, 2012. https://doi.org/10.1155/2012/872187

Information

Published: 2012
First available in Project Euclid: 4 April 2013

zbMATH: 1242.35191
MathSciNet: MR2926885
Digital Object Identifier: 10.1155/2012/872187

Rights: Copyright © 2012 Hindawi

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Vol.2012 • No. SI11 • 2012
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