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We study the validity of an averaging principle for a slow-fast system ofstochastic reaction diffusion equations. We assume here that the coefficientsof the fast equation depend on time, so that the classical formulation of theaveraging principle in terms of the invariant measure of the fast equation isnot anymore available. As an alternative, we introduce the time dependingevolution family of measures associated with the fast equation. Under theassumption that the coefficients in the fast equation are almost periodic, theevolution family of measures is almost periodic. This allows to identify theappropriate averaged equation and prove the validity of the averaging limit.

Averaging principle for non autonomous slow-fast systems of stochastic RDEs: the almost periodic case