The Long-time Behavior Of The Solutions For Stochastic Plate Equation

In this master dissertation, we mainly consider the long-time behavior of the solutions for the stochastic strongly damped plate equation with additive noise and the stochastic plate equation with strong damping and white noise.In the first chapter, some preliminary results and important conclusions that we will used in this thesis are presented.In the second chapter, we investigate the existence of random attractor for the following stochastic strongly damped plate equation with additive noise: where Ω is a bounded smooth domain in Rn(n=5), and{Wj}jm=1are inde-pendent two-sided real-valued Wiener processes. In order to obtain a bounded attractor for the random dynamical system, we using the method of defining a spatial average in this chapter to show the existence of random attractors.In the third chapter, we consider the long-time behavior of the solutions for the following stochastic plate equation with strong damping and white noise:where f2is a bounded smooth domain in Rn(n=5), and W(t) is a scalar Gaussian white noise. We prove the asymptotic regularity of the solution applying the method of decomposing operator and obtain the existence ofnonempty compact random attractor.