Metastability and exit problems for systems of stochastic reaction–diffusion equations

In this paper we develop a metastability theory for class of stochastic reaction–diffusion equations exposed to small multiplicative noise. We consider the case where unperturbed equation features multiple asymptotically stable equilibria. When system is perturbations, it likely stay near one equilibrium long period time but will eventually transition neighborhood another equilibrium. are interested in studying exit from full domain attraction (in function space) surrounding an and, therefore, do not assume that uniform This means boundary allowed contain saddles and limit cycles. Our method proof purely infinite dimensional, is, go through finite dimensional approximations. addition, address noise case, impose gradient type assumptions on nonlinearity. prove large deviations logarithmic asymptotics shape, also characterizing most probable set shapes solutions at attraction.