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
    PublisherSpringer New York LLC
    Pages177-200
    Number of pages24
    Volume229
    ISBN (Print)9783319749280
    DOIs
    Publication statusPublished - 2018 Jan 1
    EventInternational conference on Stochastic Partial Differential Equations and Related Fields, SPDERF 2016 - Bielefeld, Germany
    Duration: 2016 Oct 102016 Oct 14

    Other

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

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    Keywords

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

    ASJC Scopus subject areas

    • Mathematics(all)

    Cite this

    Denis, C., Funaki, T., & Yokoyama, S. (2018). Curvature motion perturbed by a direction-dependent colored noise. In Stochastic Partial Differential Equations and Related Fields - In Honor of Michael Röckner SPDERF, 2016 (Vol. 229, pp. 177-200). Springer New York LLC. https://doi.org/10.1007/978-3-319-74929-7_9