Stochastic perturbations of the Allen-Cahn equation

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8 Citations (Scopus)

Abstract

Consider the Allen-Cahn equation with small diffusion f2 perturbed by a space time white noise of intensity a. In the limit, cr/e2 -}0, solutions converge to the noise free problem in the L? 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.

Original languageEnglish
Pages (from-to)1-19
Number of pages19
JournalElectronic Journal of Differential Equations
Volume2000
Issue number47
Publication statusPublished - 1 Dec 2000

Keywords

  • Asymptotics
  • Dynamics of phase-boundaries
  • Stochastic partial differential equations

ASJC Scopus subject areas

  • Analysis

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