Large deviations and approximations for slow–fast stochastic reaction–diffusion equations

A large deviation principle is derived for a class of stochastic reaction–diffusion partial differential equations with slow–fast components. The result shows that the rate function is exactly that of the averaged equation plus the fluctuating deviation which is a stochastic partial differential equation with small Gaussian perturbation. This result also confirms the effectiveness of the approximation of the averaged equation plus the fluctuating deviation to the slow–fast stochastic partial differential equations.