Generation and motion of interfaces in one-dimensional stochastic Allen-Cahn equation

Abstract

In this paper we study a sharp interface limit for a stochastic reaction-diffusion equation. We consider the case that the noise is a space-time white noise multiplied by a small parameter and a smooth function which has a compact support. We show a generation of interfaces for one-dimensional stochastic Allen-Cahn equation with general initial values. We prove that interfaces are generated in a time of logarithmic order. After the generation of interfaces, we connect it to the motion of interfaces which was investigated by Funaki for special initial values.

20 pages

Cited by in corpus (2)

• Generation of interfaces for multi-dimensional stochastic Allen-Cahn equation with a noise smooth in space
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