Mathematical Physics, Analysis and Geometry

, Volume 14, Issue 2, pp 101–114 | Cite as

Persistence Properties and Unique Continuation of Solutions to a Two-component Camassa–Holm Equation

Article

Abstract

We will consider a two-component Camassa–Holm system which arises in shallow water theory. The present work is mainly concerned with persistence properties and unique continuation to this new kind of system, in view of the classical Camassa–Holm equation. Firstly, it is shown that there are three results about these properties of the strong solutions. Then we also investigate the infinite propagation speed in the sense that the corresponding solution does not have compact spatial support for t > 0 though the initial data belongs to \(C_{0}^{\infty}(\Bbb{R})\).

Keywords

Two-component Camassa–Holm equation Persistence properties Propagation speed 

Mathematics Subject Classifications (2010)

37L05 35Q58 26A12 

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Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  1. 1.Department of MathematicsEast China Normal UniversityShanghaiChina
  2. 2.Department of MathematicsZhejiang Normal UniversityJinhuaChina

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