Blow-up phenomena and global existence for the nonuniform weakly dissipative b-equation

被引：11
|
作者：
Niu, Weisheng [2 ]
Zhang, Shuanghu [1 ]
机构：
[1] Southwest Univ, Dept Math, Chongqing 400715, Peoples R China
[2] Lanzhou Univ, Sch Math & Stat, Lanzhou 730000, Peoples R China
来源：
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2011年 / 374卷 / 01期
关键词：
The nonuniform weakly dissipative; b-equation; Blow-up; Decay; SHALLOW-WATER EQUATION; WELL-POSEDNESS; INTEGRABLE EQUATION; GEODESIC-FLOW; CAMASSA-HOLM; WAVES; BREAKING; FAMILY; DECAY;
D O I：
10.1016/j.jmaa.2010.08.002
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We first establish the local well-posedness for the nonuniform weakly dissipative b-equation which includes both the weakly dissipative Camassa-Holm equation and the weakly dissipative Degasperis-Procesi equation as its special cases. We then study the blow-up phenomena and the long time behavior of the solutions. Two blow-up-results are established for certain initial profiles. Moreover, two sufficient conditions for the decay of the solutions are presented. (C) 2010 Elsevier Inc. All rights reserved.
引用
收藏
页码：166 / 177
页数：12
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