### 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 |
---|---|

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 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

### Cite this

**Singular Limit for Stochastic Reaction-Diffusion Equation and Generation of Random Interfaces.** / Funaki, Tadahisa.

Research output: Contribution to journal › Article

*Acta Mathematica Sinica, English Series*, vol. 15, no. 3, pp. 407-438.

}

TY - JOUR

T1 - Singular Limit for Stochastic Reaction-Diffusion Equation and Generation of Random Interfaces

AU - Funaki, Tadahisa

PY - 1999

Y1 - 1999

N2 - 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.

AB - 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.

KW - Randomly perturbed motion

KW - Reaction-diffusion equations

KW - Singular limit

UR - http://www.scopus.com/inward/record.url?scp=0347117402&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0347117402&partnerID=8YFLogxK

M3 - Article

VL - 15

SP - 407

EP - 438

JO - Acta Mathematica Sinica, English Series

JF - Acta Mathematica Sinica, English Series

SN - 1439-8516

IS - 3

ER -