Pullback Attractors for the Boussinesq-Beam Equation with Time Delay

XU Guigui; WANG Libo; LIN Guoguang

doi:10.6054/j.jscnun.2020016

Journal of South China Normal University (Natural Science Edition) > 2020 > 52(1): 104-111. > DOI: 10.6054/j.jscnun.2020016

XU Guigui, WANG Libo, LIN Guoguang. Pullback Attractors for the Boussinesq-Beam Equation with Time Delay[J]. Journal of South China Normal University (Natural Science Edition), 2020, 52(1): 104-111. DOI: 10.6054/j.jscnun.2020016

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Pullback Attractors for the Boussinesq-Beam Equation with Time Delay

1.
School of Science, Kaili University, Kaili 556011, China
2.
School of Mathematics and Statistics, Yunnan University, Kunming 650091, China

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Received Date: April 27, 2019
Available Online: March 21, 2021

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Abstract

Abstract

The existence of pullback attractors for the Boussinesq-Beam equation with time delay is handled with the concept of contractive function and some related method. Firstly, the existence of a pullback absorbing set is verified by taking the inner product and estimating the inequalities. Then the specific energy function is constructed and the method of contractive functions is used to prove that the process $\{U(t, \tau)\}_{t \geqslant \tau}$ in $C_{D(A), V}$ produced by the Boussinesq-Beam equation with time delay possess compactness. Finally, the existence of pullback attractors in $C_{D(A), V}$ for the process $\{U(t, \tau)\}_{t \geqslant \tau}$ is proved.
- time delay,
- pullback absorbing set,
- compactness,
- pullback attractor

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