Infinite propagation speed for a two component Camassa-Holm equation

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October 2009, 12(3): 597-606. doi: 10.3934/dcdsb.2009.12.597

Infinite propagation speed for a two component Camassa-Holm equation

1.	School of Mathematical Sciences, Dublin City University, Glasnevin, Dublin 9, Ireland

Received April 2009 Revised June 2009 Published July 2009

Abstract
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This paper is concerned with the solutions of a two-component generalisation of the Camassa-Holm equation. We examine the propagation behaviour of compactly supported solutions, namely whether solutions which are initially compactly supported will retain this property throughout their time of evolution. In the negative case, where we show that solutions have an infinite speed of propagation, we present a description of how the solutions retain weaker properties throughout their existence time, namely they decay at an exponentially fast rate for the duration of their existence.

Keywords: Hunter-Saxton, compactly supported., Camassa-Holm, propagation speed, Two-component.

Mathematics Subject Classification: Primary: 35Q53, 35B6.

Citation: David Henry. Infinite propagation speed for a two component Camassa-Holm equation. Discrete & Continuous Dynamical Systems - B, 2009, 12 (3) : 597-606. doi: 10.3934/dcdsb.2009.12.597

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