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

TL;DR

This paper proves the existence of random attractors for a broad class of stochastic partial differential equations driven by various types of additive noise, including classical and fractional Brownian motion, with applications to multiple SPDE models.

Contribution

It extends the theory of random attractors to SPDEs driven by general additive noise, including non-Brownian types, and analyzes cases with single-point attractors and attraction speed bounds.

Findings

Existence of random attractors for diverse SPDEs established.

Inclusion of space-time fractional Brownian motion and Lévy noise as perturbations.

Bounds for the speed of attraction to the attractor derived.

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 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.