带非线性阻尼的非自治Berger方程的时间依赖拉回吸引子

doi:10.6040/j.issn.1671-9352.0.2020.656

《山东大学学报(理学版)》 ›› 2021, Vol. 56 ›› Issue (6): 30-41.doi: 10.6040/j.issn.1671-9352.0.2020.656

• • 上一篇

带非线性阻尼的非自治Berger方程的时间依赖拉回吸引子

杜亚利,汪璇^*

西北师范大学数学与统计学院, 甘肃兰州 730070

发布日期:2021-06-03
作者简介:杜亚利(1995— ),女,硕士研究生,研究方向为无穷维动力系统. E-mail:279813885@qq.com*通信作者简介:汪璇(1973— ), 女, 博士, 教授,研究方向为非线性微分方程和无穷维动力系统. E-mail:wangxuan@nwnu.edu.cn
基金资助:
国家自然科学基金资助项目(11761062,11961059,12061062)

Pullback attractor for the non-autonomous Berger equation with nonlinear damping

DU Ya-li, WANG Xuan^*

College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, Gansu, China

Published:2021-06-03

摘要/Abstract

摘要： 考虑带有非线性阻尼和时间依赖外力项的Berger方程解的渐近性。运用收缩函数以及渐近先验估计的方法,证明了时间依赖拉回吸引子的存在性。

关键词: Berger方程, 时间依赖拉回吸引子, 收缩函数, 非线性阻尼

Abstract: This paper investigates the asymptotic of solution for the Berger equation with nonlinear damping and time-dependent external force. Then the existence time-dependent pullback attractor is proved by use of contractive function and asymptotic priori estimation.

Key words: Berger equation, time-dependent pullback attractor, contractive function, nonlinear damping

中图分类号:

O175.27

杜亚利,汪璇. 带非线性阻尼的非自治Berger方程的时间依赖拉回吸引子[J]. 《山东大学学报(理学版)》, 2021, 56(6): 30-41.

DU Ya-li, WANG Xuan. Pullback attractor for the non-autonomous Berger equation with nonlinear damping[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2021, 56(6): 30-41.

参考文献

[1] BERGER H M. A new approach to the analysis of large deflections of plates[J]. J Appl Mech, 1955, 22: 465-472.
[2] DMITRIEVA Ž N. On the theory of nonlinear oscillations of the rectangular plates[J]. Izv Vyssh Uchebn Zaved, Mat, 1978(8): 62-66.
[3] XIAO Haibin. Asymptotic dynamics of plate equation with a critical exponent on unbounded domain[J]. Nonl Anal, 2009, 70(3): 1288-1301.
[4] YANG Lu, ZHONG Chengkui. Global attractor for plate equation with nonlinear damping[J]. Nonlinear Analysis, 2008, 69: 3802-3810.
[5] YANG Lu, WANG Xuan. Existence of attractors for the non-autonomous Berger equation with nonlinear damping[J]. Electronic Differential Equations, 2017, 2017: 278-1-278-14.
[6] 王芳平,马巧珍. 带线性记忆的弱阻尼吊桥方程拉回吸引子的存在性[J]. 吉林大学学报(理学版), 2018, 56(6):1307-1314. WANG Fangping, MA Qiaozhen. Existence of pullback attractors for weakly damped suspension bridge equations with memory[J]. Journal of Jilin University(Natural Science Edition), 2018, 56(6):1308-1314.
[7] CONTIN M, PATA V, TEMAM R. Attractors for processes on time-dependent spaces and applications to wave equation[J]. Journal of Differential Equations, 2013, 255(6): 1254-1277.
[8] 刘亭亭, 马巧珍. Plate方程时间依赖全局吸引子的存在性[J]. 华东师范大学学报(自然科学版), 2016(2): 35-44. LIU Tingting, MA Qiaozhen. Existence of time-dependent global attractors for plate equations[J]. Journal of East China Normal University(Natural Science), 2016(2): 35-44.
[9] 刘亭亭, 马巧珍. 非自治 Plate 方程时间依赖强拉回吸引子的存在性[J]. 数学年刊, 2017, 38A(2): 125-144. LIU Tingting, MA Qiaozhen. The existence of time-dependent strong pullback attractors for non-autonmous plate equations[J]. Chinese Journal of Contemporary Mathematics, 2017, 38A(2): 125-144.
[10] MENG Fengjuan, WU Jie, ZHAO Chunxiang. Time-dependent global attractor for extensible Berger equation[J]. Journal of Mathematical Analysis and Applications, 2019, 469(2): 1045-1069.
[11] SUN Chunyou, CAO Daoming, DUAN Jinqiao. Non-autonomous dynamics of wave equations with nonlinear damping and critical nonlinearity[J]. Nonlinearity, 2006, 19(11): 1645-2655.
[12] FEIREISL E. Global attractors for damped wave equations with supercritical exponent[J]. Journal of Differential Equations, 1995, 116: 431-447.
[13] KHANMAMEDOV A K. Global attractors for Von Karman equations with nonlinear interior dissipation[J]. J Math Anal Appl, 2006, 318(1):92-101.
[14] PATA V, ZELIK S. Smooth attractors for strongly damped wave equations[J]. Nonlinearity, 2006, 19(7): 1495-1506.
[15] WANG Yunhai. Pullback attractors for strongly damped wave equations with critical exponent[J]. Nonl Anal, 2008, 68(2): 365-376.

多维度评价

Viewed

Full text

Abstract

Cited

Shared

Discussed

带非线性阻尼的非自治Berger方程的时间依赖拉回吸引子

Pullback attractor for the non-autonomous Berger equation with nonlinear damping

PDF (PC)

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 3

多维度评价

本文评价

推荐阅读 0

[1]	罗李平,罗振国,曾云辉. 一类带阻尼项的拟线性双曲系统的(全)振动性问题[J]. 山东大学学报（理学版）, 2016, 51(6): 73-77.
[2]	罗李平, 罗振国, 曾云辉. 带脉冲效应的拟线性双曲系统(强)振动性分析[J]. 山东大学学报（理学版）, 2015, 50(03): 57-61.
[3]	吴晓霞,马巧珍. 带有强阻尼的波方程在Rⁿ上的时间依赖吸引子[J]. 《山东大学学报(理学版)》, 2021, 56(6): 22-29.