Random attractors for a class of stochastic partial differential equations driven by general additive noise
Analysis of PDEs
2011-07-21 v2 Dynamical Systems
Probability
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 -Laplace equation and stochastic porous media equations. Besides classical Brownian motion, we also include space-time fractional Brownian Motion and space-time L\'evy 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.
Cite
@article{arxiv.1010.4641,
title = {Random attractors for a class of stochastic partial differential equations driven by general additive noise},
author = {Benjamin Gess and Wei Liu and Michael Roeckner},
journal= {arXiv preprint arXiv:1010.4641},
year = {2011}
}
Comments
30 pages