Attractors For Stochastic Reaction-Diffusion Equation With Multipilacative Noises And Their Hausdorff Dimensions

This thesis is devoted to the study for attractors for a stochastic reaction-diffusion equation with multiplicative noises and their Hausdorff dimensions.Firstly, the equation is transformed into a random differential equation, By the Galerkin method and the invertibility of the transform, the almost surely well-posedness of the stochastic reaction-diffusion equation is obtained and it determines a stochastic dynamical system (SDS). Secondly, the SDS possesses an absorbing set and is asymptotically compact. So, the SDS owns stochastic attractors. Thirdly, by the definition of differentiability, it is checked that the SDS is almost surely differentiable on the stochastic attractors. Finally, a upper bound of the Hausdorff dimensions of the stochastic attractors is obtained by verifying the two conditions given in estimating Hausdorff dimensions.