一类弱耗散b-族系统解的持续性研究

刘思淼 郁胜旗

摘 要：本文研究了一類带有弱耗散项的b-族系统解的持续性问题。我们通过引入权重函数，运用能量方法证明了二元b-族系统的强解具备如下持续性质：如果系统的初值是指数衰减的，那么在解的最大存在时刻内，系统的解也是指数衰减的，并且衰减速率与初值相同。

关键词：b-族系统;权函数;能量方法;持续性

Persistence property for a weakly dissipative b-family system

LIU Simiao  YU Shengqi*

School of Science， Nantong University， Nantong 226019， China

Abstract： This paper mainly concerns about the persistence property of solution for a weakly dissipative b-family system. By introduction of the weight function， we use the energy method to prove that the strong solution to this system posses the following persistence property： If the initial data decays exponentially with respect to the spatial variable， then the solution will decay exponentially with the same rate during its maximum existence time.

Keywords： B-family system; Weight function; Energy method; Persistence property