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

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