The local and global existence of solutions for a generalized Camassa-Holm equation

被引：0
|
作者：
Lai, Shao Yong [1 ]
Li, Nan [1 ]
Zhang, Jian [2 ]
机构：
[1] Southwestern Univ Finance & Econ, Dept Math, Chengdu 610074, Peoples R China
[2] Sichuan Normal Univ, Dept Math, Chengdu 610066, Peoples R China
来源：
ACTA MATHEMATICA SINICA-ENGLISH SERIES | 2013年 / 29卷 / 04期
关键词：
Existence of global solutions; Camassa-Holm type equation; Pseudoparabolic regularization method; SHALLOW-WATER EQUATION; DEGASPERIS-PROCESI EQUATION; TRAVELING-WAVE SOLUTIONS; BLOW-UP PHENOMENA; WELL-POSEDNESS; WEAK SOLUTIONS; INTEGRABLE EQUATION; SCATTERING PROBLEM; PEAKON SOLUTIONS; DGH EQUATION;
D O I：
10.1007/s10114-013-1419-6
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
A fully nonlinear generalization of the Camassa-Holm equation is investigated. Using the pseudoparabolic regularization technique, its local well-posedness in Sobolev space H (s) (a"e) with is established via a limiting procedure. Provided that the initial momentum (1 -a, (x) (2) )u (0) satisfies the sign condition, u (0) a H (s) (a"e) and u (0) epsilon L (1)(a"e), the existence and uniqueness of global solutions for the equation are shown to be true in the space C([0,a);H (s) (a"e)) a (c) C (1)([0,g8);H (s-1)(a"e)).
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页码：757 / 776
页数：20
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