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Asymptotic analysis on the Euler Poisson equation arising in plasma physics

Research Project

Project/Area Number 23654062
Research Category

Grant-in-Aid for Challenging Exploratory Research

Allocation TypeMulti-year Fund
Research Field Global analysis
Research InstitutionTokyo Institute of Technology

Principal Investigator

SHINYA Nishibata  東京工業大学, 情報理工学(系)研究科, 教授 (80279299)

Project Period (FY) 2011-04-28 – 2015-03-31
Project Status Completed (Fiscal Year 2014)
Budget Amount *help
¥3,510,000 (Direct Cost: ¥2,700,000、Indirect Cost: ¥810,000)
Fiscal Year 2013: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2012: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2011: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Keywordsオイラー方程式 / ポアソン方程式 / 双曲型保存則 / ボーム・シース条件 / 境界層 / 双曲型保存
Outline of Final Research Achievements

We proved the asymptotic stability of the stationary solution to an Euler Poisson equation arising in the plasma physics under the Bohm sheath condition. We also obtained the convergence rate towards the stationary solution subject to the initial condition. In addition we made numerical experiments. Precisely, we confirmed numerically that the solution converges to the stationary solution as time tends to infinity. Here we compared several numerical schemes. In conclusion, we see that the roe scheme makes a best performance in stability of scheme and convergence speed.

Report

(5 results)
  • 2014 Annual Research Report   Final Research Report ( PDF )
  • 2013 Research-status Report
  • 2012 Research-status Report
  • 2011 Research-status Report
  • Research Products

    (24 results)

All 2015 2014 2013 2012 2011

All Journal Article (9 results) (of which Peer Reviewed: 9 results) Presentation (15 results) (of which Invited: 11 results)

  • [Journal Article] The mathematical justi cation of the Bohm criterion in plasma physics2015

    • Author(s)
      Shinya Nishibata, Masashi Ohnawa, and Masahiro Suzuki
    • Journal Title

      Advanced Studies in Pure Mathematics

      Volume: -

    • Related Report
      2014 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Nonlinear stability of boundary layer solutions to the Euler-Poisson equations in plasma physics2014

    • Author(s)
      Shinya Nishibata, Masashi Ohnawa, and Masahiro Suzuki
    • Journal Title

      AIMS Series on Applied Mathematics

      Volume: 8 Pages: 817-822

    • Related Report
      2014 Annual Research Report
    • Peer Reviewed
  • [Journal Article] The mathematical justication of the Bohm criterion in plasma physics2014

    • Author(s)
      Shinya Nishibata, Masashi Ohnawa and Masahiro Suzuki
    • Journal Title

      Advanced Studies in Pure Mathematics

      Volume: 64

    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Journal Article] Energy estimate for a linear symmetric hyperbolic-parabolic system in half line2013

    • Author(s)
      T. Nakamura and S. Nishibata
    • Journal Title

      Kinet. Relat. Models

      Volume: 6 Issue: 4 Pages: 883-892

    • DOI

      10.3934/krm.2013.6.883

    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Journal Article] The mathematical justification of the Bohm criterion in plasma physics2013

    • Author(s)
      Shinya Nishibata, Masashi Ohnawa and Masahiro Suzuki
    • Journal Title

      Advanced Studies in Pure Mathematics

      Volume: 未定

    • Related Report
      2012 Research-status Report
    • Peer Reviewed
  • [Journal Article] Asymptotic stability of boundary layers to the Euler-Poisson equations arising in plasma physics2012

    • Author(s)
      Shinya Nishibata, Masashi Ohnawa and Masahiro Suzuki
    • Journal Title

      SIAM J. Math. Anal.

      Volume: 44 Issue: 1 Pages: 761-790

    • DOI

      10.1137/s0036141097322169

    • Related Report
      2012 Research-status Report
    • Peer Reviewed
  • [Journal Article] Asymptotic stability of boundary layers to the Euler-Poisson equations arising in plasma physics2012

    • Author(s)
      Shinya Nishibata, Masashi Ohnawa, Masahiro Suzuki
    • Journal Title

      SIAM J.Math.Anal.

      Volume: 44 Issue: 2 Pages: 761-790

    • DOI

      10.1137/110835657

    • Related Report
      2011 Research-status Report
    • Peer Reviewed
  • [Journal Article] Hierarchy of semiconductor equations: relaxation limits with initial layers for large initial data2011

    • Author(s)
      Shinya Nishibata, Masahiro Suzuki
    • Journal Title

      MSJ Memoir

      Volume: 26 Pages: 1-113

    • Related Report
      2011 Research-status Report
    • Peer Reviewed
  • [Journal Article] Stationary wave associated with an inflow problem in the half line for viscous heat-conductive gas2011

    • Author(s)
      T.Nakamura, et al
    • Journal Title

      Journal of Hyperbolic Differential Equations

      Volume: 8 Issue: 04 Pages: 651-670

    • DOI

      10.1142/s0219891611002524

    • Related Report
      2011 Research-status Report
    • Peer Reviewed
  • [Presentation] Stability of stationary solutions to hyperbolic-parabolic systems in half space and the convergence rate2014

    • Author(s)
      Shinya Nishibata
    • Organizer
      スペクトル・散乱理論とその周辺
    • Place of Presentation
      数理解析研究所, 京都大学
    • Year and Date
      2014-10-15 – 2014-10-17
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Presentation] Asymptotic stability of stationary solutions to the Euler-Poisson equation in plasma physics"2014

    • Author(s)
      Shinya Nishibata
    • Organizer
      Wayamba International Conference 2014
    • Place of Presentation
      Wayamba University of Sri Lanka
    • Year and Date
      2014-08-29 – 2014-08-30
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Presentation] Asymptotic stability of stationary solutions to hyperbolic-parabolic systems in half space and the convergence rate2014

    • Author(s)
      Shinya Nishibata
    • Organizer
      Summer Workshop on Kinetic Theory and Gas Dynamics
    • Place of Presentation
      Stanford University
    • Year and Date
      2014-07-22
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Presentation] Stationary Solutions to Symmetric Hyperbolic-parabolic Systems in Half Space2014

    • Author(s)
      Shinya Nishibata
    • Organizer
      10th AIMS International Conference on Dynamical Systems, Differential Equations and Applications
    • Place of Presentation
      Universidad Aut\'onoma de Madrid,Madrid, Spain
    • Year and Date
      2014-07-07
    • Related Report
      2014 Annual Research Report
  • [Presentation] Asymptotic stability of stationary solutions to symmetric hyperbolic-parabolic systems in half space and the convergence rate2014

    • Author(s)
      Shinya Nishibata
    • Organizer
      2014 International Conference on Nonlinear Evolutionary Partial Differential Equations
    • Place of Presentation
      Shanghai Jiao Tong University
    • Year and Date
      2014-06-06
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Presentation] Asymptotic stability of stationary solutions to the Euler-Poisson equation arising in plasma physics2014

    • Author(s)
      Shinya Nishibata
    • Organizer
      IMS Workshop on Nonlinear PDEs from Fluids and related Topics
    • Place of Presentation
      The Chinese University of Hong Kong
    • Related Report
      2013 Research-status Report
    • Invited
  • [Presentation] Stationary waves to symmetric hyperbolic-parabolic systems in half space2013

    • Author(s)
      Shinya Nishibata
    • Organizer
      The 9th Japanese-German International Workshop on Mathematical Fluid Dynamics
    • Place of Presentation
      Waseda University
    • Related Report
      2013 Research-status Report
    • Invited
  • [Presentation] Boundary layer to symmetric hyperbolic parabolic systems2013

    • Author(s)
      Shinya Nishibata
    • Organizer
      International Workshop on Nonlinear Analysis: Fluid Dynamics and Kinetic Theory
    • Place of Presentation
      Academia Sinica, Taipei
    • Related Report
      2013 Research-status Report
    • Invited
  • [Presentation] Boundary layer solution to the hyperbolic-parabolic system2013

    • Author(s)
      Shinya Nishibata
    • Organizer
      International Conference on the Mathematical Fluid Dynamics
    • Place of Presentation
      ホテル日航奈良 (奈良県)
    • Related Report
      2012 Research-status Report
    • Invited
  • [Presentation] Stationary solution to symmetric hyperbolic-parabolic system in half space2012

    • Author(s)
      Shinya Nishibata
    • Organizer
      International Conference on Nonlinear Analysis: Evolutionary PDE and Kinetic Theory
    • Place of Presentation
      Academia Sinica, Tai-Pei, Taiwan
    • Related Report
      2012 Research-status Report
    • Invited
  • [Presentation] Stationary solution to symmetric hyperbolic-parabolic system in half space2012

    • Author(s)
      Shinya Nishibata
    • Organizer
      Kinetic Theory and Related Fields: Theoretical and Numerical Approaches
    • Place of Presentation
      京都大学 (京都府)
    • Related Report
      2012 Research-status Report
    • Invited
  • [Presentation] Asymptotic Stability of Stationary Solutions to the Euler-Poisson Equations in Plasma Physics2012

    • Author(s)
      Shinya Nishibata
    • Organizer
      International conference on nonlinear evolutionary partial differential equations
    • Place of Presentation
      Shanghai Jiao Tong University, P. R. China
    • Related Report
      2012 Research-status Report
    • Invited
  • [Presentation] Asymptotic stability of boundary layers to the Euler-Poisson equation in plasma physics2011

    • Author(s)
      Shinya Nishibata
    • Organizer
      The Equadiff 2011
    • Place of Presentation
      Loughborough University, UK
    • Related Report
      2011 Research-status Report
  • [Presentation] Mathematical analysis on semiconductor equations: model hierarchy and Asymptotic behavior2011

    • Author(s)
      Shinya Nishibata
    • Organizer
      Nonlinear dynamics in partial differential equations(招待講演)
    • Place of Presentation
      九州大学
    • Related Report
      2011 Research-status Report
  • [Presentation] Asymptotic stability of boundary layers to the Euler-Poisson equation arising in plasma physic2011

    • Author(s)
      Shinya Nishibata
    • Organizer
      The 8-th East Asia Conference on Partial Differential Equations(招待講演)
    • Place of Presentation
      POSTECH, Korea
    • Related Report
      2011 Research-status Report

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Published: 2011-08-05   Modified: 2019-07-29  

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