We study an Allen–Cahn equation perturbed by a multiplicative stochastic noise that is white in time and correlated in space. Formally this equation approximates a stochastically forced mean curvature flow. We derive a uniform bound for the diffuse surface area, prove the tightness of solutions in the sharp interface limit, and show the convergence to phase-indicator functions.
|Journal||Stochastic Partial Differential Equations: Analysis and Computations|
|Publication status||Published - 1 Mar 2013|