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Mathematical Analysis for the phenomena governed by conservation Laws

Research Project

Project/Area Number 22740103
Research Category

Grant-in-Aid for Young Scientists (B)

Allocation TypeSingle-year Grants
Research Field Global analysis
Research InstitutionGifu University

Principal Investigator

TSUGE Naoki  岐阜大学, 教育学部, 准教授 (30449897)

Project Period (FY) 2010-04-01 – 2014-03-31
Project Status Completed (Fiscal Year 2013)
Budget Amount *help
¥1,950,000 (Direct Cost: ¥1,500,000、Indirect Cost: ¥450,000)
Fiscal Year 2012: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2011: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2010: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Keywords圧縮性オイラー方程式 / ノズル流 / 圧縮性流体 / ラバル管 / 半導体 / 時間大域解の存在 / 不変領域 / 解の一意性 / 流体力学 / 定常解の一意存在 / ラバール管 / 保存則 / 偏微分方程式 / 超音速流 / 半導体の方程式 / 解の存在
Research Abstract

First, we considered the motion of electrons and positive ions in a semiconductor and studied the one-dimensional stationary problem. We supplied the Dirichlet boundary condition, which represents the Ohmic contact. Moreover, we treated with a large doping profile, which is the fixed ion in the semiconductor. Then we proved the existence and uniqueness of a solution.
Next, we were concerned with the motion of gas in a nozzle. The phenomena were governed by the compressible Euler equations. We treated with the Cauchy problem for the equations. Then, we proved the global existence of a solution for the Laval nozzle and large data in 2011 (resp. the general nozzle and small data in 2012).

Report

(4 results)
  • 2013 Final Research Report ( PDF )
  • 2012 Annual Research Report
  • 2011 Annual Research Report
  • 2010 Annual Research Report
  • Research Products

    (19 results)

All 2014 2013 2012 2011 2010

All Journal Article (6 results) (of which Peer Reviewed: 5 results) Presentation (13 results)

  • [Journal Article] Isentropic gas flow for the compressible Euler equation in a nozzle2014

    • Author(s)
      N. Tsuge
    • Journal Title

      Archive for Rational Mechanics and Analysis

      Volume: 印刷中

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Isentropic gas flow for the compressible Euler equation in a nozzle2013

    • Author(s)
      Tsuge Naoki
    • Journal Title

      Arch. Ration. Mech. Anal

      Volume: 209, no.2 Issue: 2 Pages: 365-400

    • DOI

      10.1007/s00205-013-0637-5

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Existence of global solutions for unsteady isentropic gas flow in a Laval nozzle2012

    • Author(s)
      Tsuge Naoki
    • Journal Title

      Arch. Ration. Mech. Anal

      Volume: 205, no.1 Issue: 1 Pages: 151-193

    • DOI

      10.1007/s00205-012-0503-x

    • Related Report
      2013 Final Research Report 2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Uniqueness of Stationary Solutions to a One-dimensional Bipolar Hydro dynamic Model of Semiconductors2011

    • Author(s)
      Naoki Tsuge
    • Journal Title

      数理解析研究所講究録

      Volume: 1730 Pages: 18-27

    • Related Report
      2010 Annual Research Report
  • [Journal Article] Existence and uniqueness of stationary solutions to a onedimensional bipolar hydrodynamic model of semiconductors2010

    • Author(s)
      Tsuge Naoki
    • Journal Title

      Nonlinear Anal

      Volume: 73, no.3 Issue: 3 Pages: 779-787

    • DOI

      10.1016/j.na.2010.04.015

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Existence and uniqueness of stationary solutions to a one-dimensional bipolar hydrodynamic model of semiconductors2010

    • Author(s)
      Naoki Tsuge
    • Journal Title

      Nonlinear Analysis

      Volume: 73 Pages: 779-787

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Presentation] Motion of the inviscid gas through a nozzle - Existence of a time global solution and invariant regions -2014

    • Author(s)
      Tsuge Naoki
    • Organizer
      IMS Workshop on Nonlinear PDEs from Fluids and Related Topics
    • Place of Presentation
      香港中文大学
    • Year and Date
      2014-03-25
    • Related Report
      2013 Final Research Report
  • [Presentation] Motion of the inviscid gas through a nozzle - Existence of a time global solution and invariant regions -2013

    • Author(s)
      Tsuge Naoki
    • Organizer
      Fourth Japan-China Workshop on Mathematical Topics from Fluid Mechanics
    • Place of Presentation
      東京工業大学
    • Year and Date
      2013-09-19
    • Related Report
      2013 Final Research Report
  • [Presentation] ノズル内の気体の運動-時間大域解の存在と不変領域-2013

    • Author(s)
      柘植直樹
    • Organizer
      日本数学会
    • Place of Presentation
      京都大学
    • Related Report
      2012 Annual Research Report
  • [Presentation] Existence of Global Solutions for Unsteady Isentropic Gas Flow in a Laval Nozzle2012

    • Author(s)
      Tsuge Naoki
    • Organizer
      第7回日独流体数学国際研究集会
    • Year and Date
      2012-11-07
    • Related Report
      2013 Final Research Report
  • [Presentation] Existence of global solutions for unsteady isentropic gas ow in a laval nozzle2012

    • Author(s)
      Tsuge Naoki
    • Organizer
      京都大学数理解析研究所(代表者 : 井口達雄)
    • Year and Date
      2012-07-06
    • Related Report
      2013 Final Research Report
  • [Presentation] ラバール管内の気体の運動-時間大域解の存在-2012

    • Author(s)
      柘植直樹
    • Organizer
      日本数学会
    • Place of Presentation
      東京理科大学神楽坂キャンパス
    • Year and Date
      2012-03-29
    • Related Report
      2011 Annual Research Report
  • [Presentation] Existence of global solutions for unsteady isentropic gas flow in a Laval nozzle2012

    • Author(s)
      Naoki Tsuge
    • Organizer
      京都大学研究所研究集会「流体と気体の数学解析」
    • Place of Presentation
      京都大学数理解析研究所
    • Related Report
      2012 Annual Research Report
  • [Presentation] Existence of Global Solutions for Unsteady Isentropic Gas Flow in a Laval Nozzle2012

    • Author(s)
      Naoki Tsuge
    • Organizer
      第7 回 日独流体数学国際研究集会
    • Place of Presentation
      早稲田大学
    • Related Report
      2012 Annual Research Report
  • [Presentation] Stationary problems to a one-dimensional bipolar hydrodynamic models of semiconductors2010

    • Author(s)
      Tsuge Naoki
    • Organizer
      流体と気体の数学解析(代表者 : 愛木豊彦)
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2010-10-13
    • Related Report
      2013 Final Research Report
  • [Presentation] Stationary Problems to a One-dimensional Bipolar Hydrodynamic Models of Semiconductors2010

    • Author(s)
      Naoki Tsuge
    • Organizer
      現象の数理解析に向けた非線形発展方程式とその周辺
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2010-10-13
    • Related Report
      2010 Annual Research Report
  • [Presentation] Existence and uniqueness of stationary solutions to a onedimensional bipolar hydrodynamic models of semiconductors2010

    • Author(s)
      Tsuge Naoki
    • Organizer
      流体と気体の数学解析(代表者 : 隠居良行)
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2010-07-07
    • Related Report
      2013 Final Research Report
  • [Presentation] Existence and uniqueness of stationary solutions to a one-dimensional bipolar hydrodynamic models of semiconductors2010

    • Author(s)
      Naoki Tsuge
    • Organizer
      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
      2010-07-07
    • Related Report
      2010 Annual Research Report
  • [Presentation] 1次元の半導体の流体力学モデルの定常問題について 古典解の存在と一意性2010

    • Author(s)
      柘植直樹
    • Organizer
      理論応用力学講演会
    • Place of Presentation
      日本学術会議
    • Year and Date
      2010-06-09
    • Related Report
      2010 Annual Research Report

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Published: 2010-08-23   Modified: 2019-07-29  

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