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Stochastic analysis of fractal stochastic Burgers equation

Research Project

Project/Area Number 25800060
Research Category

Grant-in-Aid for Young Scientists (B)

Allocation TypeMulti-year Fund
Research Field Basic analysis
Research InstitutionShinshu University

Principal Investigator

XIE Bin  信州大学, 学術研究院理学系, 准教授 (50510038)

Project Period (FY) 2013-04-01 – 2016-03-31
Project Status Completed (Fiscal Year 2015)
Budget Amount *help
¥4,030,000 (Direct Cost: ¥3,100,000、Indirect Cost: ¥930,000)
Fiscal Year 2015: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2014: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2013: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Keywords確率解析 / 確率偏微分方程式 / entropy solution / intermittency / 分数冪ラプラスアン / 確率エントロピー解 / 大偏差原理 / Intermittency / 確率熱方程式 / 分数階ラプラス作用素 / 確率バーガー型方程式 / Levy過程
Outline of Final Research Achievements

We mainly investigated the uniqueness and various properties to the solution of stochastic partial differential equations, by the approach of stochastic analysis. We first considered the uniqueness of stochastic fractal Burgers equations. By introducing a new kind of definition of solution, stochastic entropy solution, we proved the uniqueness of the solution in some proper state space. We also studied long time behavior relative to intermittency of stochastic reaction-diffusion equation driven by space-time white noise on a bounded domain, which are essentially depending on the estimate of its fundamental solution.

Report

(4 results)
  • 2015 Annual Research Report   Final Research Report ( PDF )
  • 2014 Research-status Report
  • 2013 Research-status Report
  • Research Products

    (11 results)

All 2016 2015 2014 2013

All Journal Article (2 results) (of which Peer Reviewed: 2 results,  Acknowledgement Compliant: 1 results) Presentation (9 results) (of which Int'l Joint Research: 1 results,  Invited: 8 results)

  • [Journal Article] Some effects of the noise intensity upon non-linear stochastic heat equations on [0,1]2016

    • Author(s)
      Bin XIE
    • Journal Title

      Stochastic Process. Appl.

      Volume: 126 Issue: 4 Pages: 1184-1205

    • DOI

      10.1016/j.spa.2015.10.014

    • Related Report
      2015 Annual Research Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Fluctuations in an evolutional model of two-dimensional Young diagrams2013

    • Author(s)
      T. Funaki, M. Sasada, M. Sauer and B. Xie
    • Journal Title

      Stoch. Proc. Appl.

      Volume: 123 Issue: 4 Pages: 1229-1275

    • DOI

      10.1016/j.spa.2012.12.005

    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Presentation] 確率偏微分方程式に関する長時間の振る舞いについて2016

    • Author(s)
      Bin XIE
    • Organizer
      マルコフ過程とその周辺
    • Place of Presentation
      ヴェルク横須賀(神奈川県横須賀市)
    • Year and Date
      2016-01-09
    • Related Report
      2015 Annual Research Report
  • [Presentation] Effects of the noise intensity upon stochastic heat equations with linear growth coefficients2015

    • Author(s)
      Bin XIE
    • Organizer
      Seminar Of Morningside Center of Mathematics
    • Place of Presentation
      Morningside Center of Mathematics, CAS,China
    • Year and Date
      2015-09-24
    • Related Report
      2015 Annual Research Report
    • Invited
  • [Presentation] Some properties of stochastic partial differential equations2015

    • Author(s)
      Bin XIE
    • Organizer
      2015 Peking University Youth Probability Forum
    • Place of Presentation
      Peking University, China
    • Year and Date
      2015-07-06
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Limit theorems on Young diagrams2014

    • Author(s)
      Bin XIE
    • Organizer
      Seminar of Mathematical Sciences,
    • Place of Presentation
      Tusinghua University,China
    • Year and Date
      2014-09-18
    • Related Report
      2014 Research-status Report
    • Invited
  • [Presentation] Fractal Burgers equations with Gaussian type noises2014

    • Author(s)
      Bin XIE
    • Organizer
      数学セミナー
    • Place of Presentation
      Tusinghua University, China
    • Year and Date
      2014-05-08
    • Related Report
      2014 Research-status Report
    • Invited
  • [Presentation] Some limit problems for an evolutional model of 2-D Young diagrams2013

    • Author(s)
      XIE BIN
    • Organizer
      International Conference on Statistics and Probability
    • Place of Presentation
      Chengdou, China
    • Related Report
      2013 Research-status Report
    • Invited
  • [Presentation] Limit problems for the evolutional models of two-dimensional Young diagrams2013

    • Author(s)
      XIE BIN
    • Organizer
      Probability Seminar
    • Place of Presentation
      Morningside Center of Mathematics
    • Related Report
      2013 Research-status Report
    • Invited
  • [Presentation] Entropy solution for the stochastic fractal Burgers equation2013

    • Author(s)
      XIE BIN
    • Organizer
      PDE Seminar
    • Place of Presentation
      University of Science and Technology of China
    • Related Report
      2013 Research-status Report
    • Invited
  • [Presentation] SPDEs deduced from evolutional models of two-dimensional Young diagrams2013

    • Author(s)
      XIE BIN
    • Organizer
      RIMS 研究集会「非圧縮性粘性流体の数理解析」
    • Place of Presentation
      京都大学数理解析研究所
    • Related Report
      2013 Research-status Report
    • Invited

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Published: 2014-07-25   Modified: 2019-07-29  

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