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首页> 外文期刊>Journal of Mathematical Physics >Blow-up, blow-up rate and decay of the solution of the weakly dissipative Camassa-Holm equation
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Blow-up, blow-up rate and decay of the solution of the weakly dissipative Camassa-Holm equation

机译:弱耗散Camassa-Holm方程解的爆破,爆破速率和衰减

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摘要

In this paper, we mainly study several problems on the weakly dissipative periodic Camassa-Holm equation. At first, the local well-posedness of the equation is obtained by Kato's theorem, a necessary and sufficient condition of the blow-up of the solution and some criteria guaranteeing the blow-up of the solution are established. Then, the blow-up rate of the solution is discussed. Moreover, we prove that the equation has global solutions and these global solutions decay to zero as time goes to infinite provided the potentials associated to their initial date are of one sign. (c) 2006 American Institute of Physics.
机译:在本文中,我们主要研究关于弱耗散周期Camassa-Holm方程的几个问题。首先,利用加藤定理求出方程的局部适定性,建立了爆破解的充要条件,并建立了保证爆破解的一些准则。然后,讨论了溶液的爆炸率。此外,我们证明了方程具有全局解,并且随着与其初始日期相关的电位为一个符号,随着时间到无穷大,这些全局解将衰减为零。 (c)2006年美国物理研究所。

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