超线性阻尼项和Kirchhoff项对解衰减速率的影响  

Effect of Superlinear Damping Term andKirchhoff Term to Decay Rate of Solutions

作　　者：李仲庆 郭斌 高文杰[2] LI Zhongqing;GUO Bin;GAO Wenjie(School of Mathematics and Statistics,Guizhou University of Finance and Economics,Guiyang 550025,China;College of Mathematics,Jilin University,Changchun 130012,China)

机构地区：[1]贵州财经大学数学与统计学院,贵阳550025 [2]吉林大学数学学院,长春130012

出　　处：《吉林大学学报(理学版)》2025年第1期9-14,共6页Journal of Jilin University:Science Edition

基　　金：吉林省科技厅发展计划项目(批准号:2015020458NY).

摘　　要：考虑一类具Kirchhoff项的非局部波动方程解的衰减速率.首先,通过对解Sobolev范数建立加权估计,克服超临界阻尼项带来经典乘子法失效的困难.其次,利用加权乘子法证明当阻尼项为超临界阻尼时,所研究问题能量泛函为对数衰减,完全不同于线性阻尼的指数衰减和次临界阻尼的多项式衰减.We considered the decay rate of solutions to a class of nonlocal wave equations with Kirchhoff term.Firstly,by establishing weighted estimates of the Sobolev norm,the difficulty of classical multiplier method failure caused by supercritical damping term could be overcome.Secondly,by using the weighted multiplier method to prove that the energy functional of the studied problem decayed logarithmically when the damping term was supercritical damping,which was totally different from both exponential decay of linear damping and polynomial decay of subcritical damping.

关 键 词：非局部方程 加权乘子法 衰减估计 

分 类 号：O175.27[理学—数学]