# Ergodicity for a class of semilinear stochastic partial differential equations

## TL;DR

This paper proves the existence and uniqueness of invariant measures for certain semilinear stochastic PDEs with multiplicative noise, applicable to models like stochastic Burgers and reaction-diffusion equations on bounded domains.

## Contribution

It establishes foundational ergodic properties for a broad class of semilinear SPDEs driven by multiplicative noise, including key examples like Burgers and reaction-diffusion equations.

## Key findings

- Existence of invariant measures for the considered SPDEs
- Uniqueness of these invariant measures
- Applicability to various SPDE models such as Burgers and reaction-diffusion equations

## Abstract

In this paper, we establish the existence and uniqueness of invariant measures for a class of semilinear stochastic partial differential equations driven by multiplicative noise on a bounded domain. The main results can be applied to SPDEs of various types such as the stochastic Burgers equation and the reaction-diffusion equations perturbed by space-time white noise.