  In this paper, we develop the averaging principle for a class of
two-time-scale stochastic reaction-diffusion equations driven by Wiener
processes and Poisson random measures. We assume that all coefficients of the
equation have polynomial growth, and the drift term of the equation is
non-Lipschitz. Hence, the classical formulation of the averaging principle
under the Lipschitz condition is no longer available. To prove the validity of
the averaging principle, the existence and uniqueness of the mild solution are
proved firstly. Then, the existence of time-dependent evolution family of
measures associated with the fast equation is studied, by which the averaged
coefficient is obtained. Finally, the validity of the averaging principle is
verified.
