Averaging Principle for Systems of Reaction-Diffusion Equations with Polynomial Nonlinearities Perturbed by Multiplicative Noise

We prove the validity of an averaging principle for a class of systems of slow-fast reaction-diffusion equations with the reaction terms in both equations having polynomial growth, perturbed by a noise of multiplicative type. The models we have in mind are the stochastic Fitzhugh–Nagumo equation arising in neurophysiology and the Ginzburg–Landau equation arising in statistical mechanics.