Curvature motion perturbed by a direction-dependent colored noise

Clément Denis, Tadahisa Funaki, Satoshi Yokoyama

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Citation (Scopus)

Abstract

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.

Original languageEnglish
Title of host publicationStochastic Partial Differential Equations and Related Fields - In Honor of Michael Röckner SPDERF, 2016
EditorsGerald Trutnau, Andreas Eberle, Walter Hoh, Moritz Kassmann, Martin Grothaus, Wilhelm Stannat
PublisherSpringer New York LLC
Pages177-200
Number of pages24
ISBN (Print)9783319749280
DOIs
Publication statusPublished - 2018
EventInternational conference on Stochastic Partial Differential Equations and Related Fields, SPDERF 2016 - Bielefeld, Germany
Duration: 2016 Oct 102016 Oct 14

Publication series

NameSpringer Proceedings in Mathematics and Statistics
Volume229
ISSN (Print)2194-1009
ISSN (Electronic)2194-1017

Other

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

Keywords

  • Colored noise
  • Motion by mean curvature
  • Stochastic partial differential equation
  • Wong–Zakai theorem

ASJC Scopus subject areas

  • Mathematics(all)

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