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

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

2010-10-22

arxiv.org/abs/1010.4641v2

J. Differential Equations 251 (2011), 1225--1253

Mathematics

Analysis of PDEs

30 pages

Scientific paper

10.1016/j.jde.2011.02.013

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 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.

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