Strong averaging principles for a class of non-autonomous slow-fast systems of SPDEs with polynomial growth

TL;DR

This paper establishes strong averaging principles for non-autonomous slow-fast stochastic reaction-diffusion systems driven by Poisson measures, proving convergence of the slow component to an averaged equation under polynomial growth conditions.

Contribution

It extends averaging principles to non-autonomous SPDEs with polynomial growth and local Lipschitz conditions, including the existence, uniqueness, and convergence analysis.

Findings

Existence and uniqueness of mild solutions for the considered SPDEs.

Development of an averaged equation for non-autonomous systems.

Proof of strong convergence of the slow component to the averaged solution.

Abstract

In this work, we study a class of non-autonomous two-time-scale stochastic reaction-diffusion equations driven by Poisson random measures, in which the coefficients satisfy the polynomial growth condition and local Lipschitz condition. First, the existence and uniqueness of the mild solution are proved by constructing auxiliary equations and using the technique of stopping time. Then, consider that the time dependent of the coefficients, the averaged equation is redefined by studying the existence of time-dependent evolution family of measures associated with the frozen fast equation. Further, the slow component strongly converges to the solution of the corresponding averaged equation is verified by using the classical Khasminskii method.