一类耗散型Camassa-Holm方程的解的爆破  

THE BLOW-UP OF THE SOLUTIONS FOR A DISSIPATIVE CAMASSA-HOLM EQUATION

作　　者：徐能[1] 李子宝[1] 

机构地区：[1]云南师范大学数学学院,云南昆明650092

出　　处：《数学杂志》2013年第5期871-880,共10页Journal of Mathematics

基　　金：国家自然科学基金(10961029)资助项目

摘　　要：本文研究了带耗散项λuxx的Camassa-Holm方程的局部适定性和爆破现象.由Kato定理得到局部适定性的结果,证明了解的爆破机制,并且证明了当初值满足一定条件时解发生爆破,最后研究了爆破解的爆破率.In this paper, we study the local well-posedness and the blow-up phenomenon of the Gamassa-Holm equation with dissipative term λuxx. By using the Kato＇s, the local well-posedness is obtained and the blow-up mechanism is proved, two results of blow-up solutions with certain initial profiles are established, the blow-up rate of the blow-up solutions is studied finally.

关 键 词：耗散型Camassa-Holm方程 局部适定性 解的爆破 爆破率 

分 类 号：O175.29[理学—数学]