Attractors For Stochastic Plate Equation With Strongly Damped And Critical Exponent

This paper considers the existence of random attractors for the dynamical systems determined by stochastic plate equation with strongly damped and nonlinear critical in an unbounded and bounded domain, respectively. The paper is divided into three parts.The first chapter states the background and some basic concepts.The second chapter considers the asymptomatic behavior of the stochastic plate equation with strong damping and critical exponent under homogeneous Neumann boundary condition in a bounded set with a smooth boundary. By introducing an O-U process and applying transformation, the stochastic plate equation with white multiplicative noise can be transformed into a random equation with no noise, in which the sample can be regarded as a common parameter, thus, the original equation determines a random dynamical system. The splitting technique is introduced to deal with the asymptotical compactness of the dynamical system.The last chapter investigates the existence of random attractor for the dynamical systems determined by a stochastic plate equation with multiplicative noise under strong damping and nonlinear exponent in unbounded domain. The tail-estimates method is introduced to verify the asymptotical compactness of the stochastic equation. Finally, the existence of random attractor for the dynamical system is obtained.