Abstract

We study random perturbations of a reaction-diffusion equation with a unique stable equilibrium and solutions that blow-up in finite time. If the strength of the perturbation epsilon > 0 is small and the initial data is in the domain of attraction of the stable equilibrium, the 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 time (but exponentially large in epsilon(-2)). Moreover, for initial data in the domain of explosion we show that the explosion times converge to the one of the deterministic solution. (C) 2017 Elsevier B.V. All rights reserved.