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

Research output: Contribution to journalArticle

18 Citations (Scopus)

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 languageEnglish
Pages (from-to)407-438
Number of pages32
JournalActa Mathematica Sinica, English Series
Volume15
Issue number3
Publication statusPublished - 1999
Externally publishedYes

Fingerprint

Stochastic Reaction-diffusion Equations
Singular Limit
Phase Separation
Phase separation
Curve
Additive noise
Additive Noise
Reaction-diffusion Equations
Bounded Domain
Curvature
Converge
Motion
Term

Keywords

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

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Cite this

@article{523cc03259cb4817b920b576dcc52c28,
title = "Singular Limit for Stochastic Reaction-Diffusion Equation and Generation of Random Interfaces",
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.",
keywords = "Randomly perturbed motion, Reaction-diffusion equations, Singular limit",
author = "Tadahisa Funaki",
year = "1999",
language = "English",
volume = "15",
pages = "407--438",
journal = "Acta Mathematica Sinica, English Series",
issn = "1439-8516",
publisher = "Springer Verlag",
number = "3",

}

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

AN - SCOPUS:0347117402

VL - 15

SP - 407

EP - 438

JO - Acta Mathematica Sinica, English Series

JF - Acta Mathematica Sinica, English Series

SN - 1439-8516

IS - 3

ER -