Abstract
AbstractThis paper investigates mainly the asymptotic behavior of the nonautonomous random dynamical systems generated by the plate equations driven by colored noise defined on$\mathbb{R}^{n}$Rn. First, we prove the well-posedness of the equation in the natural energy space. Secondly, we define a continuous cocycle associated with the solution operator. Finally, we establish the existence and uniqueness of random attractors of the equation by the uniform tail-ends estimates methods and the splitting technique.
Funder
National Natural Science Foundation of China，China
Publisher
Springer Science and Business Media LLC
Subject
Algebra and Number Theory,Analysis
Reference37 articles.
1. Springer Monographs in Mathematics;L. Arnold,1998
2. Barbosaa, A.R.A., Ma, T.F.: Long-time dynamics of an extensible plate equation with thermal memory. J. Math. Anal. Appl. 416, 143–165 (2014)
3. Gu, A., Guo, B., Wang, B.: Long term behavior of random Navier-Stokes equations driven by colored noise. Discrete Contin. Dyn. Syst., Ser. B 25, 2495–2532 (2020)
4. Gu, A., Wang, B.: Asymptotic behavior of random FitzHugh-Nagumo systems driven by colored noise. Discrete Contin. Dyn. Syst., Ser. B 23, 1689–1720 (2018)
5. Khanmamedov, A.K.: Existence of global attractor for the plate equation with the critical exponent in an unbounded domain. Appl. Math. Lett. 18, 827–832 (2005)