  We study small random perturbations by additive space-time white noise of a
reaction-diffusion equation with a unique stable equilibrium and solutions
which blow up in finite time. We show that for initial data in the domain of
attraction of the stable equilibrium the perturbed system exhibits metastable
behavior: its time averages remain stable around this equilibrium until an
abrupt and unpredictable transition occurs which leads to explosion in a finite
(but exponentially large) time. On the other hand, for initial data in the
domain of explosion we show that the explosion time of the perturbed system
converges to the explosion time of the deterministic solution.
