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Asymptotic analysis for systems of a hyperbolicparabolic type appeared in fluid dynamics

Research Project

Project/Area Number 21740100
Research Category

Grant-in-Aid for Young Scientists (B)

Allocation TypeSingle-year Grants
Research Field Basic analysis
Research InstitutionKyushu University

Principal Investigator

NAKAMURA Tohru  九州大学, 大学院・数理学研究院, 助教 (90432898)

Project Period (FY) 2009 – 2011
Project Status Completed (Fiscal Year 2011)
Budget Amount *help
¥4,030,000 (Direct Cost: ¥3,100,000、Indirect Cost: ¥930,000)
Fiscal Year 2011: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2010: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2009: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Keywords解析学 / 偏微分方程式論 / 流体力学 / 圧縮性流体 / 漸近解析 / エネルギー法 / 粘性保存則 / 境界層解 / 漸近挙動
Research Abstract

In the present research, we consider an existence and an asymptotic stability of a boundary layer solution(stationary wave) for model systems of compressible and viscous gases. More precisely, we prove the existence and the asymptotic stability of boundary layer solution for an outflow and an inflow problems of heatconductive model. Moreover, we show the existence of boundary layer solution for model systems of symmetric hyperbolicparabolic type.

Report

(4 results)
  • 2011 Annual Research Report   Final Research Report ( PDF )
  • 2010 Annual Research Report
  • 2009 Annual Research Report
  • Research Products

    (28 results)

All 2011 2010 2009 Other

All Journal Article (10 results) (of which Peer Reviewed: 7 results) Presentation (18 results)

  • [Journal Article] Stationary wave associated with an in ow problem in the half line for viscous heat-conductive gas2011

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

      J. Hyperbolic Differ. Equ.

      Volume: 8no.4 Pages: 651-670

    • Related Report
      2011 Final Research Report
  • [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 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Energy method in the partial Fourier space and application to stability problems in the half space.2011

    • Author(s)
      Y. Ueda, T. Nakamura, S. Kawashima
    • Journal Title

      J. Differential Equations

      Volume: 250 Issue: 2 Pages: 1169-1199

    • DOI

      10.1016/j.jde.2010.10.003

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Stationary waves to viscous heat-conductive gases in half space : ex-istence, stability and convergence rate, Math2010

    • Author(s)
      S. Kawashima, T. Nakamura, S. Nishibata and P. Zhu
    • Journal Title

      Models and Meth. in Appl. Sci

      Volume: No.12 Issue: 12 Pages: 2201-2235

    • DOI

      10.1142/s0218202510004908

    • Related Report
      2011 Final Research Report
  • [Journal Article] Convergence rate toward degenerate station-ary wave for compressible viscous gases2010

    • Author(s)
      T. Nakamura, Y. Ueda and S. Kawashima
    • Journal Title

      Proceedings of NACA2009

      Pages: 239-248

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Stationary waves to viscous heat-conductive gases in half space : existence, stability and convergence rate2010

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

      Math.Models and Meth.in Appl.Sci.

      Volume: 20 Pages: 2201-2235

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Convergence rate toward degenerate stationary wave for compressible viscous gases2010

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

      Proceedings of NACA2009

      Pages: 239-248

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Conver-gence rate toward planar stationary waves for compressible viscous uid in multi-dimensional half space2009

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

      SIAM J. Math. Anal

      Volume: 41No.5 Issue: 5 Pages: 1757-1791

    • DOI

      10.1137/090755357

    • Related Report
      2011 Final Research Report
  • [Journal Article] Convergence rate toward planar stationary waves for compressible viscous fluid in multi-dimensional half space2009

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

      SIAM J.Math.Anal. 41

      Pages: 1757-1791

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Asyrnptotic stability of stationary waves for symmetric hyperbolicparabolic system

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

      京都大学数理解析研究所講究録に掲載決定

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Presentation] Analysis of Partial Differential Equations2011

    • Author(s)
      T. Nakamura
    • Organizer
      Stationary wave to the sym-metric hyperbolic-parabolic system in half space, SIAM Conference on
    • Place of Presentation
      San Diego, California, USA
    • Year and Date
      2011-11-15
    • Related Report
      2011 Final Research Report
  • [Presentation] Boundary layer solution to systems of viscous conservation laws in half space2011

    • Author(s)
      T. Nakamura
    • Organizer
      Third China-Japan Workshop on Mathematical Topics from Fluid Mechanics
    • Place of Presentation
      Northwest University, Xi' an, China
    • Year and Date
      2011-10-25
    • Related Report
      2011 Final Research Report
  • [Presentation] Boundary layer solution to systems of viscous conservation laws in half space2011

    • Author(s)
      T.Nakamura
    • Organizer
      Third China-Japan Workshop on Mathematical Topics from Fluid Mechanics
    • Place of Presentation
      Northwest University, Xi'an, China(招待講演)
    • Year and Date
      2011-10-25
    • Related Report
      2011 Annual Research Report
  • [Presentation] 熱伝導圧縮性粘性流体に現れる境界層解の存在性と漸近安定性2011

    • Author(s)
      中村徹
    • Organizer
      日本流体力学会年会2011
    • Place of Presentation
      首都大学東京
    • Year and Date
      2011-09-07
    • Related Report
      2011 Annual Research Report 2011 Final Research Report
  • [Presentation] Asymptotic stability of sta-tionary waves for symmetric hyperbolic-parabolic system in half space2011

    • Author(s)
      T. Nakamura
    • Organizer
      RIMS...... RIMS研究集会流体と気体の数学解析
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2011-07-08
    • Related Report
      2011 Final Research Report
  • [Presentation] Asymptotic stability of stationary waves for symmetric hyperbolic-parabolic system in half space2011

    • Author(s)
      T.Nakamura
    • Organizer
      RIMS研究集会「流体と気体の数学解析」
    • Place of Presentation
      京都大学数理解析研究所(招待講演)
    • Year and Date
      2011-07-08
    • Related Report
      2011 Annual Research Report
  • [Presentation] Boundary layer solution for compressible viscous and heatconductive fluid in half space2011

    • Author(s)
      T. Nakamura
    • Organizer
      The 3rd Kyushu University POSTECH Joint Workshop Partial Dif ferential Equations and Fluid Dynamics
    • Place of Presentation
      POSTECH, Republic of Keora
    • Year and Date
      2011-06-17
    • Related Report
      2011 Final Research Report
  • [Presentation] Inflow and outflow problems for compressible viscous and heatconductive fluid2011

    • Author(s)
      T. Nakamura
    • Organizer
      Euskadi揖yushu Workshop on Applied Mathematics
    • Place of Presentation
      Basque Center for Applied Mathematics, Spain
    • Year and Date
      2011-03-10
    • Related Report
      2011 Final Research Report
  • [Presentation] 半空間における圧縮性粘性流体の漸近挙動について2010

    • Author(s)
      中村徹
    • Organizer
      日本数学会2010年度秋季総合分科会特別講i演
    • Place of Presentation
      名古屋大学
    • Year and Date
      2010-09-25
    • Related Report
      2011 Final Research Report
  • [Presentation] 半空間における圧縮性粘性流体の漸近挙動について2010

    • Author(s)
      中村徹
    • Organizer
      日本数学会2010年度秋季総合分科会
    • Place of Presentation
      名古屋大学(特別講演)
    • Year and Date
      2010-09-25
    • Related Report
      2010 Annual Research Report
  • [Presentation] Stationary waves for viscous heatconductive gases in half line2010

    • Author(s)
      T. Nakamura
    • Organizer
      13th Inter national Conference on Hyperbolic Problems : Theory, Numerics, Applications, Xijiao Ho tel
    • Place of Presentation
      Beijing, P. R. China
    • Year and Date
      2010-06-18
    • Related Report
      2011 Final Research Report
  • [Presentation] Stationary waves for viscous heat-conductive gases in half line2010

    • Author(s)
      T.Nakamura
    • Organizer
      13th International Conference on Hyperbolic Problems
    • Place of Presentation
      Xijiao Hotel (P.R.China)
    • Year and Date
      2010-06-18
    • Related Report
      2010 Annual Research Report
  • [Presentation] Asymptotic stability of stationary waves for viscous heatconductive gases in half line2009

    • Author(s)
      T. Nakamura
    • Organizer
      Second Japan-China Workshop on Mathematical Topics from Fluid Mechanics
    • Place of Presentation
      九州大学
    • Year and Date
      2009-11-16
    • Related Report
      2011 Final Research Report
  • [Presentation] Stationary waves for vis cons heatconductive fluid in half space2009

    • Author(s)
      T. Nakamura
    • Organizer
      RIMS研究集会流体と気体の数学解析
    • Place of Presentation
      京都大学
    • Year and Date
      2009-07-09
    • Related Report
      2011 Final Research Report
  • [Presentation] Stationary waves for viscous heat-conductive fluid in half space2009

    • Author(s)
      中村徹
    • Organizer
      RIMS研究集会「流体と気体の数学解析」
    • Place of Presentation
      京都大学
    • Year and Date
      2009-07-09
    • Related Report
      2009 Annual Research Report
  • [Presentation] 半空間における熱伝導圧縮性粘性流体の定常波について2009

    • Author(s)
      中村徹,西畑伸也,川島秀一, P. C. Zhu
    • Organizer
      第58回理論応用力学講演会,日本学術会議
    • Place of Presentation
      東京
    • Year and Date
      2009-06-11
    • Related Report
      2011 Final Research Report
  • [Presentation] Stationary waves for vis cons heatconductive fluid in half space2009

    • Author(s)
      T. Nakamura
    • Organizer
      In ternational Conference on Kinetic and Re tated Models
    • Place of Presentation
      Wuhan University, Wuhan, P. R. China
    • Year and Date
      2009-04-02
    • Related Report
      2011 Final Research Report
  • [Presentation] Stationary waves for viscous heat-conductive fluid in half space2009

    • Author(s)
      T.Nakamura
    • Organizer
      International Conference on Kinetic and Related Models
    • Place of Presentation
      Wuhan University, P.R.China
    • Year and Date
      2009-04-02
    • Related Report
      2009 Annual Research Report

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Published: 2009-04-01   Modified: 2016-04-21  

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