CONICET | Buscador de Institutos y Recursos Humanos

We study small random perturbations by additive white-noise of a spatial discretization ofa reaction?diffusion equation with a stable equilibrium and solutions that blow up in finitetime. We prove that the perturbed system blows up with total probability and establish itsorder of magnitude and asymptotic distribution. For initial data in the domain of explosionwe prove that the explosion time converges to the deterministic one while for initial datain the domain of attraction of the stable equilibrium we show that the system exhibitsmetastable behavior.