The existence of weak solutions for a  generalized Camassa-Holm equation

Shaoyong Lai; Qichang Xie; Yunxi Guo; YongHong Wu

doi:10.3934/cpaa.2011.10.45

Article Contents

2011, Volume 10, Issue 1: 45-57. Doi: 10.3934/cpaa.2011.10.45

This issue Previous Article Analysis of the Laplacian and spectral operators on the Vicsek set Next Article The obstacle problem for Monge-Ampère type equations in non-convex domains

The existence of weak solutions for a generalized Camassa-Holm equation

1.
Department of Mathematics,Sichuan Normal University, Chengdu, Department of Mathematics and Statistics,Curtin University of Technology, Perth
2.
Department of Applied Mathematics, Southwestern University of Finance and Economics, 610074, Chengdu

Received: October 2009

Revised: August 2010

Published: January 2011

Abstract / Introduction Related Papers Cited by

Abstract

A Camassa-Holm type equation containing nonlinear dissipative effect is investigated. A sufficient condition which guarantees the existence of weak solutions of the equation in lower order Sobolev space $H^s$ with $1 \leq s \leq \frac{3}{2}$ is established by using the techniques of the pseudoparabolic regularization and some prior estimates derived from the equation itself.

Keywords:

Generalized Camassa-Holm equation,
weak solution,
high order nonlinear terms,
pseudoparabolic regularization technique.

Mathematics Subject Classification: Primary: 35Q53; Secondary: 35L05.

Citation:

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