Singular limit for stochastic reaction-diffusion equation and generation of random interfaces

Singular limit is investigated for reaction-diffusion equations with an additive noise in a bounded domain of .2. The solution converges to one of the two stable phases {+1, .1} determined from the reaction term; accordingly a phase separation curve is generated in the limit. We shall derive a randomly perturbed motion by curvature for the dynamics of the phase separation curve.