Electronic Journal of Differential Equations Electron. J. Diff. Eqns., Vol. 2000(2000), No. 47, pp. 1-19.
Stochastic perturbations of the Allen-Cahn equation
Tony Shardlow
Abstract: Consider the Allen-Cahn equation with small diffusion
perturbed by a space time white noise of intensity
. In the limit,
, solutions converge to the noise free problem in the
norm. Under these conditions, asymptotic results for the evolution of phase boundaries in the deterministic setting are extended, to describe the behaviour of the stochastic Allen-Cahn PDE by a system of stochastic differential equations. Computations are described, which support the asymptotic derivation.
Submitted April 18, 2000. Published June 15, 2000.
Math Subject Classifications: 60H15, 74N20, 45M05.
Key Words: dynamics of phase-boundaries, stochastic partial differential equations, asymptotics.
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Tony Shardlow
Dept. Computer Science
University of Manchester
Oxford Road
Manchester M13 9PL, England
e-amil: shardlow@bioinf.man.ac.uk
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