Exponential stability of non-autonomous stochastic partial differential equations with finite memory

TL;DR

This paper investigates the exponential stability of nonlinear, non-autonomous stochastic PDEs with finite memory, providing criteria for stability in mean square and almost sure senses, supported by an illustrative example.

Contribution

It introduces new stability criteria for a class of stochastic PDEs with finite memory, expanding understanding of their long-term behavior.

Findings

Established criteria for exponential stability in mean square and almost sure senses.

Demonstrated the criteria with a specific example.

Extended stability analysis to non-autonomous stochastic PDEs with finite memory.

Abstract

The exponential stability, in both mean square and almost sure senses, for energy solutions to a class of nonlinear and non-autonomous stochastic PDEs with finite memory is investigated. Various criteria for stability are obtained. An example is presented to demonstrate the main results.