Persistence properties and infinite propagation for the modified2-component  Camassa--Holm equation

Xinglong Wu; Boling Guo

doi:10.3934/dcds.2013.33.3211

Article Contents

2013, Volume 33, Issue 7: 3211-3223. Doi: 10.3934/dcds.2013.33.3211

This issue Previous Article Upper semicontinuity of pullback attractors for nonautonomous Kirchhoff wave models Next Article

Persistence properties and infinite propagation for the modified 2-component Camassa--Holm equation

Xinglong Wu^1, and
Boling Guo^2,

1.
Institute of Applied Physics and Computational Mathematics, Beijing, 100088
2.
Institute of Applied Physics & Computational Math., Beijing 100088

Received: April 2012

Revised: July 2012

Published: July 2013

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Abstract

In this paper, we mainly study persistence properties and infinite propagation for the modified 2-component Camassa--Holm equation. We first prove that persistence properties of the solution to the equation provided the initial potential satisfies a certain sign condition. Finally, we get the infinite propagation if the initial datas satisfy certain compact conditions, while the solution to system (1.1) instantly loses compactly supported, the solution has exponential decay as $|x|$ goes to infinity.

Keywords:

The modified 2-component Camassa--Holm equation,
persistence properties,
compact support,
exponential decay,
infinite propagation speed.

Mathematics Subject Classification: 35G25, 35L05.

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