### Abstract

Singular limit is investigated for reaction-diffusion equations with an additive noise in a bounded domain of R2. The solution converges to one of the two stable phases {+1, -1} determined from the reaction term; accordingly a phase separation curve is generated in the limit. We shall derive a randomly perturbed motion by curvature for the dynamics of the phase separation curve.

Original language | English |
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Pages (from-to) | 407-438 |

Number of pages | 32 |

Journal | Acta Mathematica Sinica, English Series |

Volume | 15 |

Issue number | 3 |

Publication status | Published - 1999 |

Externally published | Yes |

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### Keywords

- Randomly perturbed motion
- Reaction-diffusion equations
- Singular limit

### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics