JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2022, Vol. 57 ›› Issue (4): 66-75.doi: 10.6040/j.issn.1671-9352.0.2021.248

Previous Articles    

Global attractor of Kirchhoff-type beam equation with memory

ZHANG Ying, LIU Qiang-qiang, MA Qiao-zhen*   

  1. College of Mathematice and Statistics, Northwest Normal University, Lanzhou 730070, Gansu, China
  • Published:2022-03-29

PDF (PC)

227

Abstract: By means of energy estimation and contraction function, the long time dynamic behavior of Kirchhoff beam equations with linear memory and nonlinear damping is studied, and the existence of global attractor in weak topological space is obtained, which partially extends the existing results.

Key words: linear memory, global attractor, bounded absorbing set, contraction function

CLC Number: 

  • O175.29
[1] WOINOWSKY-KRIEGER S. The effect of an axial force on the vibration of hinged bars[J]. Journal of Applied Mechanics Transactions of the ASME, 1950, 17(1):35-36.
[2] BERGER H M. A new approach to the analysis of large deflections of plates[J]. Journal of Applied Mechanics Transactions of the ASME, 1955, 22(4):465-472.
[3] JORGE S, MA T F. On a viscoelastic plate equation with history setting and perturbation of p-Laplacian type[J]. IMA Journal of Applied Mathematics, 2013(6):1130-1146.
[4] BALL J M. Initial-boundary value problems for an extensible beam[J]. Journal of Mathematical Analysis and Applications, 1973, 42(1):61-90.
[5] BALL J M. Stability theory for an extensible beam[J]. Journal of Differential Equations, 1973, 14(3):399-418.
[6] DICKEY R W. Free vibrations and dynamic buckling of the extensible beam[J]. Journal of Mathematical Analysis and Applications, 1970, 29(2):443-454.
[7] BIAZUTTI A C, CRIPPA H R. Global attractor and inertial set for the beam equation[J]. Applicable Analysis, 1994, 55(1/2):61-78.
[8] GIORGI C, NASO M G, PATA V, POTOMKIN M. Global attractors for the extensible thermoelastic beam system[J]. Journal of Differential Equations, 2009, 246(9):3496-3517.
[9] YAO Xiaobin, MA Qiaozhen, XU Ling. Global attractors for a Kirchhoff type plate equation with memory[J]. Kodai Mathematical Journal, 2017, 40(1):63-78.
[10] LIU Gongwei. The existence general decay and blow-up for a plate equation with nonlinear damping and a logarithmic source term[J]. Electronic Research Archive, 2020, 28(1):263-289.
[11] CHUESHOV I, LASIECKA I. Long-time behavior of second order evolution equations with nonlinear damping to appear memoires of AMS-2006[J]. Memoirs of the American Mathematical Society, 2008, 912(912):1-167.
[12] Al-GHARABLI M M, MESSAOUDI S A. Existence and a general decay result for a plate equation with nonlinear damping and a logarithmic source term[J]. Journal of Evolution Equations, 2018(8):105-125.
[13] YANG Lu, ZHONG Chengkui. Global attractor for plate equation with nonlinear damping[J]. Nonlinear Analysis: Theory Methods and Applications, 2008, 69(11):3802-3810.
[14] MA T F, NARCISO V. Global attractor for a model of extensible beam with nonlinear damping and source terms[J]. Nonlinear Analysis: Theory, Methods and Applications, 2010, 73(10):3402-3412.
[15] 贾澜,马巧珍. 带强阻尼的Kirchhoff型吊桥方程指数吸引子的存在性[J]. 中国科学(数学), 2018, 48(7):909-922. JIA Lan, MA Qiaozhen. Existence of strong global attractors for strongly damped Kirchoff type suspension bridge equations[J]. Scientia Sinica Mathematics, 2018, 48(7):909-922.
[16] 刘世芳,马巧珍. 具有历史记忆的阻尼吊桥方程强全局吸引子的存在性[J]. 数学物理学报,2017, 37A(4):684-697. LIU Shifang, MA Qiaozhen. Existence of strong global attractors for damped suspension bridge equations with history memory[J]. Acta Mathematica Scientia, 2017, 37A(4):684-697.
[17] 黄商商,马巧珍. 带线性记忆的阻尼耦合吊桥方程的全局吸引子[J].华东师范大学学报(自然科学版), 2018(2):1-22. HUANG Shangshang, MA Qiaozhen. Global attractors for damped coupled suspension bridge equations with linear memory[J]. Journal of East China Normal University(Natural Science), 2018(2):1-22.
[18] SUN Cunyou, CAO Daomin, DUAN Jinqiao. Non-autonomous dynamics of wave equations with nonlinear damping and critical nonlinearity[J]. Nonlinearity, 2006, 19(11):2645-2665.
[19] PATA V, ZUCCHI A. Attractors for a damped hyperbolic equation with linear memory[J]. Advances in Mathematical Sciences and Applications, 2001, 11:505-529.
[20] NAKAO M. Global attractors for nonlinear wave equations with nonlinear dissipative terms[J]. Journal of Differential Equations, 2006, 227(1):204-229.
[1] LIN Guo-guang, LI Zhuo-xi. Attractor family and dimension for a class of high-order nonlinear Kirchhoff equations [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2019, 54(12): 1-11.
[2] LIANG Xiao, WANG Linshan. Global attractor of a class of recurrent neural network with Stype distributed delays [J]. J4, 2009, 44(4): 57-60 .
Viewed
Full text


Abstract

Cited
  Shared   
  Discussed   
No Suggested Reading articles found!
Copyright 2018 © Editorial office of JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)
Supported by Beijing Magtech Co.Ltd