Stability and random attractors for a reaction-diffusion equation with multiplicative noise

Abstract

We study the asymptotic behaviour of a reaction-diffusion equation, and prove that the addition of multiplicative white noise (in the sense of Itô) stabilizes the stationary solution cursive Greek chi ≡ 0. We show in addition that this stochastic equation has a finite-dimensional random attractor, and from our results conjecture a possible bifurcation scenario.