• Search Research Projects
  • Search Researchers
  • How to Use
  1. Back to previous page

Asymptotic analysis for nonlinear dispersive and hyperbolic equations

Research Project

Project/Area Number 18740076
Research Category

Grant-in-Aid for Young Scientists (B)

Allocation TypeSingle-year Grants
Research Field Basic analysis
Research InstitutionTokyo Metropolitan University (2007-2008)
Gakushuin University (2006)

Principal Investigator

SHIMOMURA Akihiro  Tokyo Metropolitan University, 大学院・理工学研究科, 准教授 (00365066)

Project Period (FY) 2006 – 2008
Project Status Completed (Fiscal Year 2008)
Budget Amount *help
¥2,310,000 (Direct Cost: ¥2,100,000、Indirect Cost: ¥210,000)
Fiscal Year 2008: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2007: ¥700,000 (Direct Cost: ¥700,000)
Fiscal Year 2006: ¥700,000 (Direct Cost: ¥700,000)
Keywords解析学 / 偏微分方程式 / 関数解析 / 微分方程式 / 函数解析 / 関数方程式論 / 関数解析学 / 応用数学 / 応用数理
Research Abstract

本研究課題では,長距離型非線型消散項を伴うシュレディンガー方程式の解の長時間挙動(時間減衰評価や漸近形),ゲージ不変でない非線型項を伴うシュレディンガー方程式の散乱理論,4階シュレディンガー型方程式の解の長時間挙動(終値問題),シュレディンガー改良ブシネスク方程式系の散乱理論の研究を行い,研究成果を得た。得られた研究成果は,学術雑誌(査読付)に公表した。

Report

(4 results)
  • 2008 Annual Research Report   Final Research Report ( PDF )
  • 2007 Annual Research Report
  • 2006 Annual Research Report
  • Research Products

    (27 results)

All 2009 2008 2007 2006

All Journal Article (16 results) (of which Peer Reviewed: 13 results) Presentation (11 results)

  • [Journal Article] Large time behavior of solutions toSchrodinger equations with a dissipative nonlinearity for arbitrarily large initial data,2009

    • Author(s)
      Naoyasu Kita and Akihiro Shimomura
    • Journal Title

      Journal of the Mathematical Society of Japan 61

      Pages: 39-64

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Large time behavior of solutions to Schrodinger equations with a dissipative nonlinearity for arbitrarily large initial data2009

    • Author(s)
      Naoyasu Kita and Akihiro Shimomura
    • Journal Title

      Journal of Mathematical Society of Japan 61

      Pages: 39-64

    • NAID

      10024905488

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A short review of scattering for the Schrodinger-improved Boussinesq system,2008

    • Author(s)
      Akihiro Shimomura
    • Journal Title

      Hokkaido Mathematical Journal 37

      Pages: 813-823

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] A short review of scattering for the Schrodinger-improved Boussinesq system2008

    • Author(s)
      Akihiro Shimomura
    • Journal Title

      Hokkaido Mathematical Journal (Special Issue) 37巻

      Pages: 813-823

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Global existence and asymptotic behavior of solutions to the fourth order nonlinear Schrodinger type equation,2007

    • Author(s)
      Jun-ichi Segata and Akihiro Shimomura
    • Journal Title

      Communications in Applied Analysis 111

      Pages: 169-188

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Asymptotic behavior of solutions to Schrodinger equations with a subcritical dissipative nonlineaity,2007

    • Author(s)
      Naoyasu Kita and Akihiro Shimomura
    • Journal Title

      Journal of Differential Equations 242

      Pages: 192-210

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Scattering theory for the Schrodinger-improved Boussinesq system in two space dimensions,2007

    • Author(s)
      Akihiro Shimomura
    • Journal Title

      Asymptotic Analysis 51

      Pages: 167-187

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Scattering theory for the Schrodinger-improved Boussinesq system in two space dimensions2007

    • Author(s)
      Akihiro Shimomura
    • Journal Title

      Asymptotic Analysis 51

      Pages: 167-187

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Asymptotic behavior of solutions to Schrodinger equations with a subcritical dissipative nonlinearity2007

    • Author(s)
      Naoyasu Kita
    • Journal Title

      Journal of Differential Equations 242

      Pages: 192-210

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Global existence and asymptotic behavior of solutions to the fourth order nonlinear Schrodinger type equation2007

    • Author(s)
      Jun-ichi Segata
    • Journal Title

      Communications in Applied Analysis 11

      Pages: 169-188

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Asymptotics of solutions to the fourth order Schrodinger type equation with a dissipative nonlinearity,2006

    • Author(s)
      Jun-ichi Segata and Akihiro Shimomura
    • Journal Title

      Journal of Mathematics of Kyoto University 46

      Pages: 439-456

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Nonexistence of scattering states forsome quadratic nonlinear Schrodinger equations in two space dimensions2006

    • Author(s)
      Akihiro Shimomura and Yoshio Tsutsumi
    • Journal Title

      Differential and Integral Equations 19

      Pages: 1047-1060

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Asymptotic behavior of solutions for Schrodinger equations with dissipative nonlinearities2006

    • Author(s)
      Akihiro Shimomura
    • Journal Title

      Communications in Partial Differential Equations 31

      Pages: 1407-1423

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Asymptotic behavior of solutions for Schrodinger equations with dissipative nonlinearities2006

    • Author(s)
      Akihiro Shimomura
    • Journal Title

      Communications in Partial Differential Equations 31巻・9号

      Pages: 1407-1423

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Nonexistence of scattering states for some quadratic nonlinear Schrodinger equation in two space dimensions2006

    • Author(s)
      Akihiro Shimomura
    • Journal Title

      Differential and Integral Equations 19巻・9号

      Pages: 1047-1060

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Asymptotics of solutions to the fourth order Schrodinger type equation with a dissipative nonlinearity2006

    • Author(s)
      Jun-ichi Segata
    • Journal Title

      Journal of Mathematics of Kyoto University 46巻・2号

      Pages: 439-456

    • Related Report
      2006 Annual Research Report
  • [Presentation] 非線型消散項を伴うシュレディンガー方程式の任意の大きさの初期データに対する解の漸近挙動2008

    • Author(s)
      下村明洋
    • Organizer
      解析セミナー
    • Place of Presentation
      神戸大学
    • Year and Date
      2008-11-04
    • Related Report
      2008 Final Research Report
  • [Presentation] 劣臨界指数の非線型消散項を伴うシュレディンガー方程式の解の漸近挙動2008

    • Author(s)
      下村明洋
    • Organizer
      日本数学会(函数方程式論分科会), 一般講演
    • Place of Presentation
      東京工業大学
    • Year and Date
      2008-09-27
    • Related Report
      2008 Annual Research Report
  • [Presentation] Asymptotic behavior of solutions to Schrおdinger equations with subcritical nonlinear dissipation2008

    • Author(s)
      Akihiro Shimomura
    • Organizer
      研究集会
    • Year and Date
      2008-08-25
    • Related Report
      2008 Final Research Report
  • [Presentation] Asymptotic behavior of solutions to Schrodinger equations with subcritical nonlinear dissipation2008

    • Author(s)
      Akihiro Shimomura
    • Organizer
      Asymptotics and Singularities in Nonlinear and Geometric Dispersive Equations
    • Place of Presentation
      Banff International Research Station, Canada
    • Year and Date
      2008-08-25
    • Related Report
      2008 Annual Research Report
  • [Presentation] 非線型シュレディンガー方程式の初期値問題と解の漸近挙動2007

    • Author(s)
      下村明洋
    • Organizer
      数理解析セミナー
    • Place of Presentation
      首都大学東京
    • Year and Date
      2007-10-18
    • Related Report
      2008 Final Research Report
  • [Presentation] Scattering for the Schrodinger -improved Boussinesq system2007

    • Author(s)
      Akihiro Shimomura
    • Organizer
      Nonlinear Wave Equations
    • Place of Presentation
      北海道大学
    • Year and Date
      2007-08-27
    • Related Report
      2008 Final Research Report
  • [Presentation] ある2次の非線型項を持つシュレディンガー方程式の通常散乱状態の非存在について2007

    • Author(s)
      下村明洋
    • Organizer
      九州関数方程式セミナー
    • Place of Presentation
      九州大学
    • Year and Date
      2007-06-22
    • Related Report
      2008 Final Research Report
  • [Presentation] 非線型シュレディンガー方程式の解の長時間挙動について2007

    • Author(s)
      下村明洋
    • Organizer
      解析学火曜セミナー
    • Place of Presentation
      東京大学
    • Year and Date
      2007-05-01
    • Related Report
      2008 Final Research Report
  • [Presentation] 消散性非線型項を持つSchrodinger方程式の解の漸近挙動について2007

    • Author(s)
      下村明洋
    • Organizer
      スペクトル・散乱理論とその周辺
    • Place of Presentation
      京都大学(数理解析研究所)
    • Year and Date
      2007-02-05
    • Related Report
      2008 Final Research Report
  • [Presentation] 消散性非線型項を持つSchrodinger方程式の解の長時間挙動について2006

    • Author(s)
      下村明洋
    • Organizer
      神楽坂解析セミナー
    • Place of Presentation
      東京理科大学
    • Year and Date
      2006-10-28
    • Related Report
      2008 Final Research Report
  • [Presentation] 2次の非線型項を持つSchrodinger方程式の通常散乱状態の非存在について2006

    • Author(s)
      下村明洋
    • Organizer
      解析セミナー
    • Place of Presentation
      筑波大学
    • Year and Date
      2006-06-14
    • Related Report
      2008 Final Research Report

URL: 

Published: 2006-04-01   Modified: 2016-04-21  

Information User Guide FAQ News Terms of Use Attribution of KAKENHI

Powered by NII kakenhi