JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2021, Vol. 56 ›› Issue (6): 30-41.doi: 10.6040/j.issn.1671-9352.0.2020.656

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

DU Ya-li, WANG Xuan*   

  1. College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, Gansu, China
  • Published:2021-06-03

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

CLC Number: 

  • O175.27
[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.
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