Singular limit for stochastic reaction-diffusion equation and generation of random interfaces

被引：29

作者：

Funaki, T ^{[1
]}

机构：

[1] Univ Tokyo, Grad Sch Math Sci, Meguro Ku, Tokyo 1538914, Japan

来源：

ACTA MATHEMATICA SINICA-ENGLISH SERIES | 1999年 / 15卷 / 03期

关键词：

singular limit; reaction-diffusion equations; randomly perturbed motion;

D O I：

10.1007/BF02650735

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Singular limit is investigated for reaction-diffusion equations with an additive noise in a bounded domain of Ra. 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. 1991MR Subject Classification 60H.

引用

页码：407 / 438

页数：32

共 31 条

[1]

Adams A, 2003, SOBOLEV SPACES

[2] DYNAMICAL FLUCTUATIONS AT THE CRITICAL-POINT - CONVERGENCE TO A NONLINEAR STOCHASTIC PDE [J].

BERTINI, L ;

PRESUTTI, E ;

RUDIGER, B ;

SAADA, E .

THEORY OF PROBABILITY AND ITS APPLICATIONS, 1994, 38 (04) :586-629

[3] ASYMPTOTIC ANALYSIS OF PDES WITH WIDEBAND NOISE DISTURBANCES, AND EXPANSION OF THE MOMENTS [J].

BOUC, R ;

PARDOUX, E .

STOCHASTIC ANALYSIS AND APPLICATIONS, 1984, 2 (04) :369-422

[4]

Chen M F, 1992, MARKOV CHAINS NONEQU

[5] Asymptotic behavior of solutions of an Allen-Cahn equation with a nonlocal term [J].

Chen, XF ;

Hilhorst, D ;

Logak, E .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 1997, 28 (07) :1283-1298

[6] A diffusion-approximation theorem in Navier-Stokes equation [J].

Clouet, JF .

STOCHASTIC ANALYSIS AND APPLICATIONS, 1996, 14 (01) :33-46

[7] REACTION DIFFUSION-EQUATIONS FOR INTERACTING PARTICLE-SYSTEMS [J].

DEMASI, A ;

FERRARI, PA ;

LEBOWITZ, JL .

JOURNAL OF STATISTICAL PHYSICS, 1986, 44 (3-4) :589-644

[8]

DEMASI A, 1994, NONLINEARITY, V7, P633, DOI 10.1088/0951-7715/7/3/001

[9] MOTION BY CURVATURE BY SCALING NONLOCAL EVOLUTION-EQUATIONS [J].

DEMASI, A ;

ORLANDI, E ;

PRESUTTI, E ;

TRIOLO, L .

JOURNAL OF STATISTICAL PHYSICS, 1993, 73 (3-4) :543-570

[10]

DEMOTTONI P, 1995, T AM MATH SOC, V347, P1533

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