Infinite propagation speed for a two component Camassa-Holm equation
Infinite propagation speed for a two component Camassa-Holm equation
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DOI：
10.3934/dcdsb.2009.12.597
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发表时间：
2009-07
影响因子：
1.2
通讯作者：
D. Henry
中科院分区：
文献类型：
--
作者：
D. Henry
本文讨论两分量广义Camassa-Holm方程的解。我们考察了紧支撑解的传播行为，即最初紧支撑的解是否会在其整个演化时间内保持这一性质。在负情形下，我们证明了解具有无限的传播速度，我们描述了解如何在其存在时间内保持较弱的性质，即它们在其存在期间以指数级的速度衰减。
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.