SPD

Abstract

We deal with a class of reaction-diffusion equations in space dimension d > 1 perturbed by a Gaussian noise which is white in time and colored in space. We assume that the noise has a small correlation radius d, so that it converges to the white noise, as d goes to zero. By using arguments of Gamma Convergence, we prove that, under suitable assumptions, the quasi potential converges to the quasi-potential corresponding to space-time white noise. We apply these results to the asymptotic estimate of the mean of the exit time of the solution of the stochastic problem from a basin of attaction of an asymptotically stable point for the unperturbed problem.