Global Existence and Blow-Up Phenomena for the Degasperis-Procesi Equation
Global Existence and Blow-Up Phenomena for the Degasperis-Procesi Equation
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DOI：
10.1007/s00220-006-0082-5
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发表时间：
2006-08
影响因子：
2.4
通讯作者：
Yue Liu;Z. Yin
中科院分区：
文献类型：
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作者：
Yue Liu;Z. Yin
本文讨论了线性DeGasperis-Procesi方程整体解的存在性和奇性形成的几个方面。对于一类初始轮廓，确定了该方程的整体强解。另一方面，研究表明，第一次爆破只能以波浪破碎的形式发生。详细地描述了解的一种新的破波机制，并建立了具有一定初始轮廓的爆破解的两个结果。
This paper is concerned with several aspects of the existence of global solutions and the formation of singularities for the Degasperis-Procesi equation on the line. Global strong solutions to the equation are determined for a class of initial profiles. On the other hand, it is shown that the first blow-up can occur only in the form of wave-breaking. A new wave-breaking mechanism for solutions is described in detail and two results of blow-up solutions with certain initial profiles are established.