Stochastic Perturbations of the Allen-Cahn Equation
Date
2000-06-15
Authors
Shardlow, Tony
Journal Title
Journal ISSN
Volume Title
Publisher
Southwest Texas State University, Department of Mathematics
Abstract
Consider the Allen-Cahn equation with small diffusion ∈² perturbed by a space time white noise of intensity σ. In the limit, σ/∈² → 0, solutions converge to the noise free problem in the L² 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.
Description
Keywords
Dynamics of phase-boundaries, Stochastic partial differential equations, Asymptotics
Citation
Shardlow, T. (2000). Stochastic perturbations of the Allen-Cahn equation. <i>Electronic Journal of Differential Equations, 2000</i>(47), pp. 1-19.
Rights
Attribution 4.0 International