具变指数非线性项的强阻尼波动方程的爆破  

Blow-up to Strongly Damped Wave Equation withVariable-Exponent Nonlinear Term

作　　者：李海霞 曹春玲[2] LI Haixia;CAO Chunling(School of Mathematics,Changchun Normal University,Changchun 130032,China;College of Mathematics,Jilin University,Changchun 130012,China)

机构地区：[1]长春师范大学数学学院,长春130032 [2]吉林大学数学学院,长春130012

出　　处：《吉林大学学报（理学版）》2024年第1期78-86,共9页Journal of Jilin University:Science Edition

基　　金：国家自然科学基金(批准号:11626044);长春师范大学人才引进启动项目(批准号:长师大RC[2016]第008号)。

摘　　要：考虑一类具变指数非线性项的强阻尼波动方程的有限时刻爆破.借助凹方法和适当选取的参数,给出该问题的一个新的爆破准则,并给出爆破时间的上下界估计.结果表明,该爆破准则特别蕴含对任意高的初始能量,该问题存在有限时刻爆破解.We considered the finite time blow-up to a strongly damped wave equation with variable-exponent nonlinear term.With the help of concave method and appropriately selected parameters,we gave a new blow-up criterion for this problem and estimated the upper and lower bounds on the blow-up time.The results show that the blow-up criterion contains special implications for any high initial energy,and the problem has a finite time blow-up solutions.

关 键 词：强阻尼 波方程 变指数非线性项 爆破 

分 类 号：O175.2[理学—数学]