We consider stochastically perturbed gradient flows in the limit when the amplitude
of random fluctuations is small relative to the typical energy scale in the system and the minima of the
energy are not isolated but form submanifolds of the phase space. In this case the limiting dynamics
may be described in terms of a diffusion process on these manifolds. We derive explicit equations for
this limiting dynamics and illustrate them on a few finite-dimensional examples. Finally, we formally
extrapolate the reduction technique to several infinite-dimensional examples and derive equations of
the stochastic kink motion in Allen-Cahn-type systems.
@article{1274816890,
author = {Fatkullin, Ibrahim and Kovacic, Gregor and Vanden-Eijnden, Eric},
title = {Reduced dynamics of stochastically perturbed gradient flows},
journal = {Commun. Math. Sci.},
volume = {8},
number = {1},
year = {2010},
pages = { 439-461},
language = {en},
url = {http://dml.mathdoc.fr/item/1274816890}
}
Fatkullin, Ibrahim; Kovacic, Gregor; Vanden-Eijnden, Eric. Reduced dynamics of stochastically perturbed gradient flows. Commun. Math. Sci., Tome 8 (2010) no. 1, pp. 439-461. http://gdmltest.u-ga.fr/item/1274816890/