Open Access
June 2010 Reduced dynamics of stochastically perturbed gradient flows
Ibrahim Fatkullin, Gregor Kovacic, Eric Vanden-Eijnden
Commun. Math. Sci. 8(2): 439-461 (June 2010).


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.


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Ibrahim Fatkullin. Gregor Kovacic. Eric Vanden-Eijnden. "Reduced dynamics of stochastically perturbed gradient flows." Commun. Math. Sci. 8 (2) 439 - 461, June 2010.


Published: June 2010
First available in Project Euclid: 25 May 2010

zbMATH: 1197.34103
MathSciNet: MR2664459

Primary: 34F05 , 60H10 , 60H15 , 93E03

Keywords: kinks , reduced dynamics , stochastic Allen-Cahn , Stochastic gradient flows

Rights: Copyright © 2010 International Press of Boston

Vol.8 • No. 2 • June 2010
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