具变时滞项的非线性波方程解的爆破  

Blow-up of solutions for a nonlinear wave equation with a time-varying delay

作　　者：崔佳楠 刘霞 CUI Jia-nan;LIU Xia(School of Mathematical Science,Shanxi University,Taiyuan 030006,China)

机构地区：[1]山西大学数学科学学院,山西太原030006

出　　处：《云南民族大学学报（自然科学版）》2020年第5期450-457,共8页Journal of Yunnan Minzu University:Natural Sciences Edition

基　　金：国家自然科学基金(11671240)。

摘　　要：研究了一类具有变时滞项的非线性波方程.通过使用乘子法并构造了合适的能量泛函,证明了当初始数据,阻尼权重,时滞项以及源项满足某些条件时,解的能量在有限时间爆破以及爆破时刻的1个上界.This paper discusses the nonlinear wave equation with a time-varying delay.The multiplicator method and structured suitable Lyapunov functional are used to prove that the solutions of the equations blow up in a finite time and found an upper bound when the initial data,the weight of damp,the delay term and source term are under suitable assumptions.

关 键 词：非线性波方程 变时滞 爆破 

分 类 号：O231.4[理学—运筹学与控制论]