  We consider a class of stochastic reaction-diffusion equations also having a
stochastic perturbation on the boundary and we show that when the diffusion
rate is much larger than the rate of reaction, it is possible to replace the
SPDE by a suitable one-dimensional stochastic differential equation. This
replacement is possible under the assumption of spectral gap for the diffusion
and is a result of averaging in the fast spatial transport. We also study the
fluctuations around the averaged motion.
