Tightness for a stochastic Allen-Cahn equation
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Date
2010-10-08
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Abstract
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.