TY - JOUR
T1 - Tightness for a stochastic Allen–Cahn equation
AU - Röger, Matthias
AU - Weber, Hendrik
PY - 2013/3/1
Y1 - 2013/3/1
N2 - 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.
AB - 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.
UR - https://www.scopus.com/pages/publications/85042154081
U2 - 10.1007/s40072-013-0004-4
DO - 10.1007/s40072-013-0004-4
M3 - Article
SN - 2194-0401
VL - 1
SP - 175
EP - 203
JO - Stochastic Partial Differential Equations: Analysis and Computations
JF - Stochastic Partial Differential Equations: Analysis and Computations
IS - 1
ER -