Blow-up of solutions to the DGH equation

被引：68
|
作者：
Zhou, Yong [1 ]
机构：
[1] E China Normal Univ, Dept Math, Shanghai 200062, Peoples R China
来源：
JOURNAL OF FUNCTIONAL ANALYSIS | 2007年 / 250卷 / 01期
基金：
中国国家自然科学基金;
关键词：
best constant; convolution problem; integrable equation; singularity;
D O I：
10.1016/j.jfa.2007.04.019
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, firstly we find best constants for two convolution problems on the unit circle via a variational method. Then we apply the best constants on a nonlinear integrable shallow water equation (the DGH equation) to give sufficient conditions on the initial data, which guarantee finite time singularity formation for the corresponding solutions. Finally, we discuss the blow-up phenomena for the nonperiodic case. (c) 2007 Elsevier Inc. All rights reserved.
引用
收藏
页码：227 / 248
页数：22
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