Asymptotic behavior of plate equations driven by colored noise on unbounded domains

Abstract

Abstract This paper investigates mainly the asymptotic behavior of the nonautonomous random dynamical systems generated by the plate equations driven by colored noise defined on R n $\mathbb{R}^{n}$ . 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.

Keywords

• Plate equation
• Colored noise
• Asymptotic compactness
• Random attractor
• Unbounded domain