# Random Attractors for Stochastic Partly Dissipative Systems

## TL;DR

This paper establishes the existence of a global random attractor for a class of coupled stochastic PDE-ODE systems with additive noise, extending the understanding of their long-term behavior.

## Contribution

It introduces a comprehensive theory for stochastic partly dissipative systems, which was previously lacking, and demonstrates its applicability through various examples.

## Key findings

- Existence of a global random attractor proven.
- Applicable to a broad class of stochastic PDE-ODE systems.
- Provides concrete examples illustrating the theory.

## Abstract

We prove the existence of a global random attractor for a certain class of stochastic partly dissipative systems. These systems consist of a partial (PDE) and an ordinary differential equation (ODE), where both equations are coupled and perturbed by additive white noise. The deterministic counterpart of such systems and their long-time behaviour have already been considered but there is no theory that deals with the stochastic version of partly dissipative systems in their full generality. We also provide several examples for the application of the theory.