Stochastic resonance in stochastic PDEs

We consider stochastic partial differential equations (SPDEs) on the one-dimensional torus, driven by space-time white noise, and with a time-periodic drift term, which vanishes two stable one unstable equilibrium branches. Each of branches approaches once per period. prove that there exists critical noise intensity, depending forcing period minimal distance between branches, such probability solutions SPDE make transitions equilibria is exponentially small for subcritical while they happen close to 1 supercritical intensity. Concentration estimates are given in $$H^s$$ Sobolev norm any $$s<\frac{1}{2}$$ . The results generalise an infinite-dimensional setting those obtained 1-dimensional SDEs [5].