Existence of Time-Dependent Global Attractors for Beam Equations

SU Xiaohu; JIANG Jinping

doi:10.21656/1000-0887.400088

Volume 41 Issue 2

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SU Xiaohu, JIANG Jinping. Existence of Time-Dependent Global Attractors for Beam Equations[J]. Applied Mathematics and Mechanics, 2020, 41(2): 195-203. doi: 10.21656/1000-0887.400088

Citation:

SU Xiaohu, JIANG Jinping. Existence of Time-Dependent Global Attractors for Beam Equations[J]. Applied Mathematics and Mechanics, 2020, 41(2): 195-203. doi: 10.21656/1000-0887.400088

Citation:

SU Xiaohu, JIANG Jinping. Existence of Time-Dependent Global Attractors for Beam Equations[J]. Applied Mathematics and Mechanics, 2020, 41(2): 195-203. doi: 10.21656/1000-0887.400088

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Existence of Time-Dependent Global Attractors for Beam Equations

doi: 10.21656/1000-0887.400088

College of Mathematics and Computer Science, Yan’an University, Yan’an, Shaanxi 716000, P.R.China

Received Date: 2019-03-06
Rev Recd Date: 2019-04-26
Publish Date: 2020-02-01

Abstract

Abstract

The existence of time-dependent global attractors for beam equations was studied. Based on the existence theorem for time-dependent global attractors, if nonlinear term f met the critical increase condition, the asymptotic compactness of process family {U(t,τ)} corresponding to the beam equations was proved with the prior estimate method and the operator decomposition method when the coefficient was related to time t.In turn, the existence and regularity of the time-dependent global attractors for beam equations were obtained.
- beam equation,
- prior estimate,
- operator decomposition,
- time-dependent global attractor

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References(15)

References

[1]	DI PLINIO F, DUANE G S, TEMAM R. Time-dependent attractor for the oscillon equation[J]. Discrete and Continuous Dynamical Systems,2011,29(1): 141-167.
[2]	CONTI M, PATA V, TEMAM R. Attractors for processes on time-dependent spaces: applications to wave equations[J]. Journal of Differential Equations,2013,255: 1254-1277.
[3]	CONTI M, PATA V. Asymptotic structure of the attractor for processes on time-dependent spaces[J]. 〖JP〗 Nonlinear Analysis: Real World Applications,2014,19(1): 1-10.
[4]	DING T, LIU Y F. Time-dependent global attractor for the nonclassical diffusion equations[J]. Applicable Analysis,2015,94: 1439-1449.
[5]	WANG Xiaoping, MA Qiaozhen. Asymptotic sturcture of time-depengdent global attractors for the nonclassical diffusion equations[J]. Journal of Sichuan University(Natural Science Edition),2016,53(3): 508-511.
[6]	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 Sciences),2016(2): 35-44.(in Chinese))
[7]	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 strongly pullback attractors for non-autonomous plate equations[J]. Chinese Annals of Mathematics,2017,38A(2): 125-144.(in Chinese))
[8]	MENG Fengxue, CAO Fengxue. Time-dependent global attractors for strongly damped wave equation with critical exponent[J]. Journal of Sichuan University(Natural Science Edition),2018,55(6): 1156-1161.
[9]	MA Q Z, WANG X P, XU L. Existence and regularity of time-dependent global attractors for the nonclassical reaction-diffusion equations with lower forcing term[J]. Boundary Value Problems,2016,16: 10. DOI: 10.1186/s13661-015-0513-3.
[10]	〖JP2〗PATE V, CONTI M. Asymptoticstructure of the attractor for process on time-dependent spaces[J]. Nonlinear Analysis: Real World Applications,2014,19: 1-10.
[11]	CONTI M, PATA V, TEMAM R. Attractors for the process on time-dependent spaces; applications to wave equations[J]. Journal of Differential Equations,2013,255(6): 1254-1277.
[12]	LIU T T, MA Q Z. Time-dependent global attractor of nonlinear evolution damping[J]. Journal of Sichuan University(Natural Science Edition), 2017,54: 917-924.
[13]	MA T F, NARCISO V, PELICER M L. Long-time behavior of a model of extensible beams with nonlinear boundary dissipations[J]. Journal of Mathematical Analysis and Application,2012,396(2): 694-703.
[14]	LEE M J. Global attractor for some beam equation with nonlinear source and damping terms[J]. East Asian Mathematical Journal,2016,32(3): 377-385.
[15]	VANDO N. Long-time behavior of a nonlinear viscoelastic beam equation with past history[J]. Mathematical Methods in the Applied Sciences,2015,38(4): 775-784.