弱耗散浅水方程的爆破现象和整体存在性

Bulletin of Mathematical Sciences and Applications Pub Date : 2014-12-01 DOI:10.18052/WWW.SCIPRESS.COM/BSMASS.12.10

Jiangbo Zhou, Jun De Chen, Wen Zhang

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引用次数: 0

摘要

首先建立了一类弱耗散浅水方程的局部适定性，该方程的特殊情况包括弱耗散Camassa-Holm方程和弱耗散Degasperis-Procesi方程。在此基础上，对一定的初始剖面导出了两个爆破结果。最后，我们研究了解的长时间行为。

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Blow-up phenomena and global existence to a weakly dissipative shallow water equation

We first establish the local well-posedness for a weakly dissipative shallow water equation which includes both the weakly dissipative Camassa-Holm equation and the weakly dissipative Degasperis-Procesi equation as its special cases. Then two blow-up results are derived for certain initial profiles. Finally, We study the long time behavior of the solutions.

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Bulletin of Mathematical Sciences and Applications

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