Random attractors for a class of stochastic partial differential equations driven by general additive noise
- Authors: Benjamin Gess, Wei Liu, Michael Roeckner
- Preprint year: 2010
- First public date: 2010-10-22
- arXiv: 1010.4641
- Status: Published
- Publication type: Journal article
- Publication year: 2011
- Journal: Journal of differential equations, 251 (2011) 4-5, pp. 1225-1253
- DOI: 10.1016/j.jde.2011.02.013
Abstract
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 considered and bounds for the speed of attraction are obtained.