Random exponential attractor for stochastic non-autonomous suspension bridge equation with additive white noise

Ling Xu; Jianhua Huang; Qiaozhen Ma

doi:10.3934/dcdsb.2021318

Article Contents

2022, Volume 27, Issue 11: 6323-6351. Doi: 10.3934/dcdsb.2021318

This issue Previous Article Existence of ground states for Schrödinger-Poisson system with nonperiodic potentials Next Article Chaotic threshold of a class of hybrid piecewise-smooth system by an impulsive effect via Melnikov-type function

Random exponential attractor for stochastic non-autonomous suspension bridge equation with additive white noise

1.
College of Mathematics and Statistics, Northwest Normal University, Lanzhou, Gansu 730070, China
2.
College of Science, National University of Defense Technology, Changsha, 410073, China

^*Corresponding author: Ling Xu
^*Corresponding author: Ling Xu

Received: September 2021

Early access: January 2022

Published: November 2022

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Abstract

In this paper, we mainly consider the existence of random attractor and random exponential attractor for stochastic non-autonomous suspension bridge equation with additive white noise. First step, the well-posedness and the existence of a random attractor for the cocycle associated with the considered system is established. Second step, the upper semicontinuity of random attractors is also provided when the coefficient of random term approaches zero. Third step, we prove the regularity of random attractor in a higher regular space by the "iteration" method. Finally, we give the existence of a random exponential attractor for the considered system, which implies the finiteness of fractal dimension of random attractor.

Keywords:

stochastic non-autonomous suspension bridge equation,
additive white noise,
regularity,
fractal dimension,
random exponential attractor.

Mathematics Subject Classification: Primary: 60H15, 35Q35; Secondary: 35B40.

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References

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