2009/11/30 by Matthias Röger, Hendrik Weber · 1 citation
Mathematics · #math.AP #math.PR #msc:60H15 #msc:53C44
paper · pdf · doi:10.1007/s40072-013-0004-4
27 pages, final Version to appear in "Stochastic Partial Differential Equations: Analysis and Computations". In Version 4, Proposition 6.3 is new. It replaces and simplifies the old propositions 6.4-6.6
arxiv created 2012/12/17 · arxiv updated 2016/06/02
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.