Tightness for a stochastic Allen--Cahn equation

Details Tightness for a stochastic Allen--Cahn equation Tightness for a stochastic Allen--Cahn equation

2009-11-30

arxiv.org/abs/0911.5706v2

Mathematics

Analysis of PDEs

26 pages Second version is more general than first, as it includes the case of infinite dimensional noise

Scientific paper

We study an Allen-Cahn equation perturbed by a multiplicative stochastic
noise which is white in time and correlated in space. Formally this equation
approximates a stochastically forced mean curvature flow. We derive uniform
energy bounds and prove tightness of of solutions in the sharp interface limit,
and show convergence to phase-indicator functions.

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