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A Random Attractor Family of the High Order Beam Equations with White Noise
School of Mathematics and Statistics, Yunnan University, Kunming, China
School of Mathematics and Statistics, Yunnan University, Kunming, China
- 1 School of Mathematics and Statistics, Yunnan University, Kunming, China
- 2 School of Mathematics and Statistics, Yunnan University, Kunming, China
International Journal of Modern Nonlinear Theory and Application·Volume 09 (2020)·Pages 51–61·Published 18 September 2020·DOI10.4236/ijmnta.2020.93004
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Abstract
In this paper, we studied a class of damped high order Beam equation stochas-tic dynamical systems with white noise. First, the Ornstein-Uhlenbeck process is used to transform the equation into a noiseless random equation with random variables as parameters. Secondly, by estimating the solution of the equation, we can obtain the bounded random absorption set. Finally, the isomorphism mapping method and compact embedding theorem are used to obtain the system. It is progressively compact, then we can prove the existence of ran-dom attractors.
KeywordsBeam Type EquationRandom AttractorWhite Noise
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