Random attractors for a class of stochastic partial differential equations driven by general additive noise

The existence of random attractors for a large class of stochastic partial differential equations (SPDE) driven by general additive noise is established. The main results are applied to various types of SPDE, as e.g. stochastic reaction–diffusion equations, the stochastic p-Laplace equation and stochastic porous media equations. Besides classical Brownian motion, we also include space-time fractional Brownian motion and space-time Lévy noise as admissible random perturbations. Moreover, cases where the attractor consists of a single point are also investigated and bounds for the speed of attraction are obtained.