具强阻尼的Sine-Gordon型吊桥方程的长时间动力学行为研究  

Research on Long-time Dynamic Behavior of the Sine-Gordon Type Suspension Bridge Equation with Strong Damping

作　　者：吕鹏辉 吕小俊 LV Penghui;LV Xiaojun(Applied Technology College,Soochow University,Suzhou,Jiangsu,China 215325)

机构地区：[1]苏州大学应用技术学院,江苏苏州215325

出　　处：《昆明学院学报》2021年第3期50-58,共9页Journal of Kunming University

基　　金：云南省教育厅科学研究基金资助项目(2020J0908).

摘　　要：在其他学者研究的基础上,根据吊桥方程和Sine-Gordon方程的特点,研究了具强阻尼的Sine-Gordon型吊桥方程的长时间动力学行为.首先在给定适当的假设条件下,利用Galerkin有限元方法得到此类方程的整体解;其次使用算子分解方法研究了该类吊桥方程的整体吸引子;最后采用将方程线性化处理的方法,得到该类吊桥方程的整体吸引子的Hausdorff维数和分形维数存在上界.Based on the research of other scholars,according to the features of suspension bridge equation and Sine-Gordon equation,we studied the long-time dynamic behavior of the Sine-Gordon type suspension bridge equation with strong damping.Firstly,the global solution of this kind of suspension bridge equation is obtained by Galerkin finite element method under the given appropriate assumptions.Then the global attractor of this kind of suspension bridge equation is obtained by operator decomposition method.Finally,the upper bound of Hausdorff dimension and fractal dimension of the global attractor is obtained by linearizing the equation.

关 键 词：Sine-Gordon型吊桥方程 整体吸引子 Hausdorff维数 分形维数 

分 类 号：O211.6[理学—概率论与数理统计]