Shardlow, Tony2020-01-072020-01-072000-06-15Shardlow, T. (2000). Stochastic perturbations of the Allen-Cahn equation. <i>Electronic Journal of Differential Equations, 2000</i>(47), pp. 1-19.1072-6691https://hdl.handle.net/10877/9141Consider 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.Text19 pages1 file (.pdf)enAttribution 4.0 InternationalDynamics of phase-boundariesStochastic partial differential equationsAsymptoticsArticle