The scaling limit for a stochastic PDE and the separation of phases

T. Funaki*

*この研究の対応する著者

研究成果査読

66 被引用数 (Scopus)

抄録

We investigate the problem of singular perturbation for a reaction-diffusion equation with additive noise (or a stochastic partial differential equation of Ginzburg-Landau type) under the situation that the reaction term is determined by a potential with double-wells of equal depth. As the parameter ε (the temperature of the system) tends to 0, the solution converges to one of the two stable phases and consequently the phase separation is formed in the limit. We derive a stochastic differential equation which describes the random movement of the phase separation point. The proof consists of two main steps. We show that the solution stays near a manifold Mε of minimal energy configurations based on a Lyapunov type argument. Then, the limit equation is identified by introducing a nice coordinate system in a neighborhood of Mε.

本文言語English
ページ(範囲)221-288
ページ数68
ジャーナルProbability Theory and Related Fields
102
2
DOI
出版ステータスPublished - 1995 6
外部発表はい

ASJC Scopus subject areas

  • 分析
  • 統計学および確率
  • 統計学、確率および不確実性

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