Article Contents
Article Contents

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

• 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 $x\equiv 0$. We show in addition that this stochastic equation has a finite-dimensional random attractor, and from our results conjecture a possible bifurcation scenario.
Mathematics Subject Classification: 35B40, 35K57, 58F12, 60H15.

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