一类b-族方程解关于初值的非一致连续依赖性  

Non-uniform Dependence on Initial Data for the Solutions of a b-Family System

作　　者：梁晓雯 郁胜旗[1] LIANG Xiaowen;YU Shengqi(School of Sciences,Nantong University,Nantong 226019,China)

机构地区：[1]南通大学理学院,江苏南通226019

出　　处：《南通大学学报（自然科学版）》2021年第1期88-94,共7页Journal of Nantong University(Natural Science Edition)　

基　　金：国家自然科学基金项目(11501309);江苏省自然科学基金项目(BK20150400)。

摘　　要：针对Besov空间中一类b-族方程柯西问题解的连续性问题,首先构建了同时带有高频项和低频项的新型逼近解序列;然后利用能量方法估计出逼近解序列的误差,并在此基础上通过对逼近解和真实解所满足的方程式作差,估计出逼近解和真实解之间的差异;最后通过证明极限意义下该差异是可以忽略的,给出了该方程的解关于初值非一致连续依赖的结论。Aiming at the continuous property of solutions to the Cauchy problem of a b-family system in Besov spaces,a new type of approximate solutions containing high and low frequency terms is first constructed.Afterwards,the error estimates of approximate solutions are derived by applying energy methods.On the basis of it the difference between the equations of the approximate solutions and real solutions are computed,and the difference between the approximate and real solutions is also presented.Finally,by proving that the difference is negligible,one manages to prove that the solution to this equation is not uniformly continuous with respect to the initial data.

关 键 词：b-族系统 逼近解序列 非一致连续依赖性 

分 类 号：O175.29[理学—数学]