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 IJMNTA  Vol.9 No.3 , September 2020
A Random Attractor Family of the High Order Beam Equations with White Noise
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.
Cite this paper: Lin, G. and Liu, J. (2020) A Random Attractor Family of the High Order Beam Equations with White Noise. International Journal of Modern Nonlinear Theory and Application, 9, 51-61. doi: 10.4236/ijmnta.2020.93004.
References

[1]   Guo, B.L. (2000) Infinite Dimensional Dynamic System. National Defense Industry Press, Beijing.

[2]   Lin, G., Chen, L. and Wang, W. (2017) Random Attractors of the Stochastuc Strongly Damped for the High Order Nonlinear Beam Type Equation. International Journal of Mordern Nonlinear Theory and Application, 6, 59-69.
https://doi.org/10.4236/ijmnta.2017.62005

[3]   Qin, C.L. and Du, J.J. (2016) Random Attractor for Strongly Damped Stochastic Beam Equation. Journal of Science of Teachers College and University, 36, 6-11.

[4]   Xu, G.G., Wang, L.B. and Lin, G.G. (2017) Random Attractors for Nonautonomous Stochastic Wave Equations with Dispersive and Dissipative Terms. Journal of Applied Functional Analysis, 19, 131-149.

[5]   Crauel, H. and Flandoli, F. (1994) Attractors for Random Dynamical Systems. Probability Theory and Related Fields, 100, 365-393.
https://doi.org/10.1007/BF01193705

[6]   Cai, D.M., Fan, X.M. and Ye, J.J. (2014) The Random Attractor of Dissipative KDV Type Equation with Multiplicative Noise Is Considered. Journal of Southwest University for Nationalities (Natural Science Edition), 40, 900-904.

[7]   Hao, H.J.J. and Zhou, S.F. (2010) Existence of Random Attractors for Strongly Demoed Stochastic Sine-Gordon Equations. Journal of Shanghai Normal University (Natural Science Edition), 39, 121-127.

[8]   Wang, R. and Li, Y.R. (2012) Random Attractor of Generalized Ginzburg-Landau Equation with Multiplicative White Noise. Journal of Southwest University for Nationalities (Natural Science Edition), 2, 34.

[9]   Cheng, Y.Y. and Li, Y.R. (2012) Random Attractor of Generalized Kuramoto-Sivashinsky Equation with Multiplicative White Noise. Journal of Southwest University for Nationalities (Natural Science Edition), 37, 27-30.

[10]   Li, X.T. and Xu, L. (2014) Existence of Random Attractors for Stochastic Delay Discrete Wave Equations. Journal of Jilin University (Science Edition), 52, 261-262.

[11]   Ban, A.L. (2018) Asymptotic Behavior of a Class of Stochastic Wave Equations. Journal of Anhui Normal University (Natural Science Edition), 41, 329-334.

[12]   Zhao, C.D. and Zhou, S.F. (2009) Sufficient Conditions for the Existence of Global Random Attractors for Stochastic Lattice Dynamical Systems and Applications. Journal of Mathematical Analysis and Applications, 354, 78-95.
https://doi.org/10.1016/j.jmaa.2008.12.036

 
 
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