Curvature motion perturbed by a direction-dependent colored noise

Clément Denis, Tadahisa Funaki*, Satoshi Yokoyama

*この研究の対応する著者

研究成果: Conference contribution

1 被引用数 (Scopus)

抄録

The aim of this paper is twofold. First we give a brief overview of several results on the deterministic and stochastic motions by mean curvature and their derivation under the so-called sharp interface limit. Then, we study the motions by mean curvature perturbed by a direction-dependent Gaussian colored noise described by V=κ + W(t, n). This part is a generalization of (Funaki, Acta Math Sin (Engl Ser), 15:407–438, 1999) [10] where the noise is independent from space. We derive a uniform moment estimate on solutions of approximating equations and prove a Wong–Zakai type convergence theorem (in law) for the SPDEs for the curvature of a convex curve in two-dimensional space before the time the curve exhibits a singularity.

本文言語English
ホスト出版物のタイトルStochastic Partial Differential Equations and Related Fields - In Honor of Michael Röckner SPDERF, 2016
編集者Gerald Trutnau, Andreas Eberle, Walter Hoh, Moritz Kassmann, Martin Grothaus, Wilhelm Stannat
出版社Springer New York LLC
ページ177-200
ページ数24
ISBN(印刷版)9783319749280
DOI
出版ステータスPublished - 2018
外部発表はい
イベントInternational conference on Stochastic Partial Differential Equations and Related Fields, SPDERF 2016 - Bielefeld, Germany
継続期間: 2016 10月 102016 10月 14

出版物シリーズ

名前Springer Proceedings in Mathematics and Statistics
229
ISSN(印刷版)2194-1009
ISSN(電子版)2194-1017

Other

OtherInternational conference on Stochastic Partial Differential Equations and Related Fields, SPDERF 2016
国/地域Germany
CityBielefeld
Period16/10/1016/10/14

ASJC Scopus subject areas

  • 数学 (全般)

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