BLOW-UP OF SOLUTIONS TO THE PERIODIC GENERALIZED MODIFIED CAMASSA-HOLM EQUATION WITH VARYING LINEAR DISPERSION

被引：3
作者：
Zhu, Min [1 ]
Wang, Ying [2 ]
机构：
[1] Nanjing Forestry Univ, Dept Math, Nanjing 210037, Jiangsu, Peoples R China
[2] Univ Elect Sci & Technol China, Dept Math, Chengdu 611731, Peoples R China
来源：
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS | 2017年 / 37卷 / 01期
关键词：
Periodic modified generalized Camassa-Holm equation; blow up; integrable equation; sign-changing momentum; varying linear dispersion; SHALLOW-WATER EQUATION; BREAKING WAVES; CAUCHY-PROBLEM; GEODESIC-FLOW; STABILITY; PERMANENT; EXISTENCE;
D O I：
10.3934/dcds.2017027
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Considered herein is the blow-up mechanism to the periodic generalized modified Camassa-Holm equation with varying linear dispersion. The first one is designed for the case when linear dispersion is absent and derive a finite-time blow-up result. The key feature is the ratio between solution and its gradient. The second one handles the general situation when the weak linear dispersion is at present. Fortunately, there exist some conserved quantities that bound the parallel to u(x)parallel to(L4) for the periodic generalized modified Camassa-Holm equation, then the breakdown mechanisms are set up for the general case.
引用
收藏
页码：645 / 661
页数：17
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