On the Cauchy problem for the two-component Dullin-Gottwald-Holm system

Yong Chen; Hongjun Gao; Yue Liu

doi:10.3934/dcds.2013.33.3407

Article Contents

2013, Volume 33, Issue 8: 3407-3441. Doi: 10.3934/dcds.2013.33.3407

This issue Previous Article Optimal partial regularity results for nonlinear elliptic systems in Carnot groups Next Article Spreading speeds of $N$-season spatially periodic integro-difference models

On the Cauchy problem for the two-component Dullin-Gottwald-Holm system

1.
School of Mathematical Sciences, Nanjing Normal University, Nanjing 210023
2.
Jiangsu Key Laboratory for NSLSCS and School of Mathematical Sciences, Nanjing Normal University, Nanjing 210046
3.
Department of Mathematics, University of Texas at Arlington, Arlington, TX 76019-0408

Received: April 30, 2012

Revised: September 30, 2012

Published: July 2013

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Abstract

Considered herein is the initial-value problem for a two-component Dullin-Gottwald-Holm system. The local well-posedness in the Sobolev space $H^{s}(\mathbb{R})$ with $s>3/2$ is established by using the bi-linear estimate technique to the approximate solutions. Then the wave-breaking criteria and global solutions are determined in $H^s(\mathbb{R}), s > 3/2.$ Finally, existence of the solitary-wave solutions is demonstrated.

Keywords:

Two-component Dullin-Gottwald-Holm system,
regularization,
wave-breaking,
global solutions,
solitary-wave solutions.

Mathematics Subject Classification: 35G25, 35L05.

Citation:

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