一类弱耗散双组份Hunter-Saxton系统的爆破与爆破率  

Blow-up and Blow-Up Rate for the Generalized Weakly Dissipative Two-Component Hunter-Saxton System

作　　者：张剑梅[1] 

机构地区：[1]江苏大学理学院数学系

出　　处：《数学的实践与认识》2014年第5期280-288,共9页Mathematics in Practice and Theory

基　　金：国家自然科学基金(11272135)

摘　　要：研究了一类周期弱耗散双组份Hunnter-Saxton系统的爆破现象.首先,给出了此类Hunnter-Saxton系统解的局部适定性及其精确的爆破机制;其次,证明了在一定的初始值下Hunnter-Saxton系统强解的几个爆破结果;最后,给出了HunnterSaxton系统强解的爆破率.This paper studies the wave-breaking phenomena for the generalized weakly dissipative two-component Hunter-Saxton system in the periodic setting, Firstly, we get the local well-posedness and precise blow-up scenario for the generalized weakly dissipative two-component Hunter-Saxton system. Secondly, we prove several blow-up results of strong solutions and results of wave-breaking solutions with certain initial profiles. Finally, we also gain the exact blow-up rate of strong solutions.

关 键 词：弱耗散 Hunnter-Saxton系统 局部适定性 爆破 爆破率 

分 类 号：O175[理学—数学]