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

On study of evolution equations with hyperbolic properties

Research Project

Project/Area Number 19340030
Research Category

Grant-in-Aid for Scientific Research (B)

Allocation TypeSingle-year Grants
Section一般
Research Field Basic analysis
Research InstitutionOsaka University

Principal Investigator

HAYASHI Nakao  大阪大学, 大学院・理学研究科, 教授 (30173016)

Co-Investigator(Kenkyū-buntansha) NISHITANI Tatsuo  大阪大学, 大学院・理学研究科, 教授 (80127117)
DOI Shinichi  大阪大学, 大学院・理学研究科, 教授 (00243006)
KUBO Hideo  大阪大学, 大学院・理学研究科, 准教授 (50283346)
Project Period (FY) 2007 – 2010
Project Status Completed (Fiscal Year 2010)
Budget Amount *help
¥13,000,000 (Direct Cost: ¥10,000,000、Indirect Cost: ¥3,000,000)
Fiscal Year 2010: ¥3,120,000 (Direct Cost: ¥2,400,000、Indirect Cost: ¥720,000)
Fiscal Year 2009: ¥3,120,000 (Direct Cost: ¥2,400,000、Indirect Cost: ¥720,000)
Fiscal Year 2008: ¥3,380,000 (Direct Cost: ¥2,600,000、Indirect Cost: ¥780,000)
Fiscal Year 2007: ¥3,380,000 (Direct Cost: ¥2,600,000、Indirect Cost: ¥780,000)
Keywords関数方程式 / シュレディンガー方程式 / クライン-ゴルドン方程式 / 漸近的振る舞い / 共鳴現象 / 散乱問題 / 臨界冪非線形項 / 散乱作用素 / 修正散乱作用素 / 非線形Klein-Gordon方程式 / 非線形Schredinger方程式 / 双曲型方程式 / 分散型方程式 / シュレデインガー方程式 / クラインーゴルドン方程式 / 固有振動数 / 非線形問題 / 非線形Klein-Gordon / 非線形Schrodinger / 臨界冪 / 消散項 / 熱方程式
Research Abstract

We studied nonlinear Schrodinger equations, nonlinear Klein-Gordon equations and their systems. Time decay and asymptotic behavior of solutions were shown. We applied these results to show existence of wave or modified wave operators. In the case of critical nonlinearities, it was shown that main terms of solutions can be represented through nonlinearities clearly.

Report

(6 results)
  • 2010 Annual Research Report   Final Research Report ( PDF )
  • 2009 Annual Research Report   Self-evaluation Report ( PDF )
  • 2008 Annual Research Report
  • 2007 Annual Research Report
  • Research Products

    (77 results)

All 2012 2011 2010 2009 2008 2007

All Journal Article (40 results) (of which Peer Reviewed: 40 results) Presentation (37 results)

  • [Journal Article] Small data scattering for a system of nonlinear Schrodinger equations2011

    • Author(s)
      N. Hayashi, C. Li and P. I. Naumkin
    • Journal Title

      Differential Equations and Applications

      Volume: 3, no.3 Pages: 415-426

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Global existence for the cubic nonlinear Schredinger equation in lower order Sobolev spaces2011

    • Author(s)
      N. Hayashi and P. I. Naumkin
    • Journal Title

      Differential Integral Equations

      Volume: 24 Pages: 801-828

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] On a system of nonlinear Schrodinger equations in 2d2011

    • Author(s)
      N. Hayashi, C. Li and P. I. Naumkin
    • Journal Title

      Differential Integral Equations

      Volume: 24 Pages: 417-434

    • Related Report
      2010 Annual Research Report 2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Wave operator for the system of the Dirac-Klein-Gordon equations2011

    • Author(s)
      N. Hayashi, M. Ikeda and P. I. Naumkin
    • Journal Title

      Math. Methods Appl. Sciences

      Volume: 34, no.8 Pages: 896-910

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Asymptotics for nonlinear heat equations2011

    • Author(s)
      N. Hayashi and P. I. Naumkin
    • Journal Title

      Nonlinear analysis

      Volume: 74, no.5 Pages: 1585-1595

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Subcritical quadratic nonlinear Schrodinger equation2011

    • Author(s)
      N. Hayashi and P. I. Naumkin
    • Journal Title

      Communications in Contemporary Mathematics

      Volume: 13 Pages: 969-1007

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Quadratic derivative nonlinear Schrodinger equations in two space dimensions2011

    • Author(s)
      Nakao Hayashi
    • Journal Title

      Nonlinear Differential Equations and Applications

      Volume: 18 Pages: 329-355

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Small data scattering for a system of nonlinear Schrodinger equations2011

    • Author(s)
      Nakao Hayashi
    • Journal Title

      Differential Equations and Applications

      Volume: 3 Pages: 415-426

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Subcritical quadratic nonlinear Schrodinger equation2011

    • Author(s)
      Nakao Hayashi
    • Journal Title

      Commun.Contemporary Math.

      Volume: 13 Pages: 969-1007

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Global existence for the cubic nonlinear Schrodinger equation in lower order Sobolev spaces2011

    • Author(s)
      Nakao Hayashi
    • Journal Title

      Differential Integral Equations

      Volume: 24 Pages: 801-828

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Analyticity for higher order nonlinear dispersive equations, GAKUTO, International Series, Mathematical Sciences and Applications2010

    • Author(s)
      N. Hayashi, K. Tomoeda and T. Yanagisawa
    • Journal Title

      Current Advances in Nonlinear Analysis and Related Topics

      Volume: 32 Pages: 111-130

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] The initial value problem for the quadratic nonlinear Klein-Gordon equation2010

    • Author(s)
      N. Hayashi and P. I. Naumkin
    • Journal Title

      Advances in Mathematical Physics

      Pages: 504324-504324

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Benjamin-Ono equation on a half-line2010

    • Author(s)
      N. Hayashi and E. Kaikina
    • Journal Title

      International Journal of Mathematics and Mathematical Sciences

      Pages: 714534-714534

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] The initial value problem for the quadratic nonlinear Klein-Gordon equation2010

    • Author(s)
      Nakao Hayashi
    • Journal Title

      Advances in Mathematical Physics

      Volume: Article ID 504324

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Benjamin-Ono equation on a half-line2010

    • Author(s)
      Nakao Hayashi
    • Journal Title

      International Journal of Mathematics and Mathematical Sciences

      Volume: Article ID 714534

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Analyticity for higher order nonlinear dispersive equations2010

    • Author(s)
      Nakao Hayashi
    • Journal Title

      GAKUTO, International Series, Mathematical Sciences and Applications

      Volume: 32 Pages: 111-130

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Wave operator for the system of the Dirac-Klein-Gordon equations2010

    • Author(s)
      Nakao Hayashi
    • Journal Title

      Math.Methods Appl.Sciences

      Volume: 34 Pages: 896-910

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Wave operators to a quadratic nonlinear Klein-Gordon equation in two space dimensions2009

    • Author(s)
      N. Hayashi and P. I. Naumkin
    • Journal Title

      Nonlinear Analysis

      Volume: 71, no.9 Pages: 3826-3833

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Asymptotics of odd solutions of quadratic nonlinear Schrodinger equations2009

    • Author(s)
      N. Hayashi and P. I. Naumkin
    • Journal Title

      J. Math. Anal. Appl.

      Volume: 359, no.1 Pages: 146-158

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Asymptotics of odd solutions for cubic nonlinear Schrodinger equations2009

    • Author(s)
      N. Hayashi and P. I. Naumkin
    • Journal Title

      J. Differential Equations

      Volume: 246, no.4 Pages: 1703-1722

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Scattering Operator for Nonlinear Klein-Gordon Equations2009

    • Author(s)
      N. Hayashi and P. I. Naumkin
    • Journal Title

      Communications in Contemporary Mathematics

      Volume: 11, no.5 Pages: 771-178

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Final state problem for the cubic nonlinear Klein-Gordon equation2009

    • Author(s)
      N. Hayashi and P. I. Naumkin
    • Journal Title

      J. Math. Phys.

      Volume: 50, no.10 Pages: 103511-103511

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Final state problem for the cubic nonlinear Klein-Gordon equation2009

    • Author(s)
      N. Hayashi, P. I. Naumkin
    • Journal Title

      J. Math. Phys. vol. 50, no. 10

      Pages: 103511-14

    • Related Report
      2009 Self-evaluation Report
    • Peer Reviewed
  • [Journal Article] Scattering Operator for Nonlinear Klein-Gordon Equations2009

    • Author(s)
      N.Hayashi
    • Journal Title

      Commum.Contemp.Math. 11

      Pages: 771-781

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Asymptotics of odd solutions for cubic nonlinear Schredinger equations2009

    • Author(s)
      N.Hayashi
    • Journal Title

      J.Differential Equations 246

      Pages: 1703-1722

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Asymptotics of odd solutions of quadratic nonlinear Schredinger equations2009

    • Author(s)
      N.Hayashi
    • Journal Title

      J.Math.Anal.Appl. 359

      Pages: 146-158

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Nonlinear scattering for a system of one dimensional nonlinear Klein-Gordon equations2008

    • Author(s)
      N. Hayashi and P. I. Naumkin
    • Journal Title

      Hokkaido Math. J.

      Volume: 37 Pages: 647-667

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Nonlinear scattering for a system of nonlinear Klein-Gordon equations2008

    • Author(s)
      N. Hayashi, P. I. Naumkin and Ratno Bagus Edy Wibowo
    • Journal Title

      J. Math. Phys.

      Volume: 49, no.10 Pages: 103501-103501

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] On the Schrodinger equation with dissipative nonlinearities of derivative type2008

    • Author(s)
      N. Hayashi, P. I. Naumkin and H. Sunagawa
    • Journal Title

      SIAM J. Math. Anal.

      Volume: 40 Pages: 278-291

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Modified wave operators for nonlinear Schrodinger equations with subcritical dissipative nonlinearities2008

    • Author(s)
      N. Hayashi and P. I. Naumkin
    • Journal Title

      Inverse Problems and Imaging

      Volume: 1, no.2 Pages: 391-398

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] The initial value problem and asymptotics of solutions for the cubic nonlinear Klein-Gordon equation2008

    • Author(s)
      N. Hayashi and P. I. Naumkin
    • Journal Title

      Zeitschrift fur Angewandte Math. und Physik

      Volume: 59, no.6 Pages: 1002-1028

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Scattering operator for the nonlinear Klein-Gordon equations in higher space dimensions2008

    • Author(s)
      N. Hayashi and P. I. Naumkin
    • Journal Title

      J. Differential Equations

      Volume: 244 Pages: 188-199

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Asymptotic properties of solutions to dispersive equation of Schredinger type2008

    • Author(s)
      N. Hayashi, P. I. Naumkin
    • Journal Title

      J. Math. Soc. Japan vol. 60

      Pages: 631-652

    • Related Report
      2009 Self-evaluation Report
    • Peer Reviewed
  • [Journal Article] The initial value problem and asymptotics of solutions for the cubic nonlinear Klein-Gordon equation2008

    • Author(s)
      N. Hayashi, P. I. Naumkin
    • Journal Title

      Zeitschrift fur Angewandte Mathematik und Physik vol. 59, no. 6

      Pages: 1002-1028

    • Related Report
      2009 Self-evaluation Report
    • Peer Reviewed
  • [Journal Article] Asymptotic properties of solutions to dispersive equation of Schrodinger type2008

    • Author(s)
      N. Hayashi
    • Journal Title

      J. Math. Soc. Japan 60

      Pages: 631-652

    • NAID

      10024331840

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On the Schrodinger equation with dissipative nonlinearities of derivative type2008

    • Author(s)
      N. Hayashi
    • Journal Title

      SIAM J. Math. Anal. 40

      Pages: 278-291

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Nonlinear scattering for a system of nonlinear Klein-Gordon equations2008

    • Author(s)
      N. Hayashi
    • Journal Title

      J. Math. Phys. 49

      Pages: 103501-24

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Scattering operator for the nonlinear Klein-Gordon equations in higher space dimensions2008

    • Author(s)
      N. Hayashi
    • Journal Title

      Journal Differential Equations 244

      Pages: 188-199

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Modified wave operators for nonlinear Schrodinger equations with subcritical dissipative nonlinearities2007

    • Author(s)
      N. Hayashi
    • Journal Title

      Inverse Problems and Imaging 1

      Pages: 391-398

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Subcritical nonlinear heat equation2007

    • Author(s)
      N. Hayashi
    • Journal Title

      Journal Differential Equations 238

      Pages: 366-380

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Presentation] Quadratic nonlinear Klein-Gordon equation in 2d2012

    • Author(s)
      林仲夫
    • Organizer
      日本数学会年会
    • Place of Presentation
      東京理科大学
    • Year and Date
      2012-03-29
    • Related Report
      2010 Annual Research Report 2010 Final Research Report
  • [Presentation] Quadratic nonlinear Klein-Gordon equations in 1D2011

    • Author(s)
      林仲夫
    • Organizer
      The 8th East Asia PDE Conference
    • Place of Presentation
      Posco International Center, Postech, Pohang(韓国)
    • Year and Date
      2011-12-21
    • Related Report
      2010 Final Research Report
  • [Presentation] Quadratic nonlinear Klein-Gordon equations in 1D2011

    • Author(s)
      林仲夫
    • Organizer
      The 8th East Asia PDE Conference
    • Place of Presentation
      Posco International Center, Postech, Pohang(韓国)(招待講演)
    • Year and Date
      2011-12-21
    • Related Report
      2010 Annual Research Report
  • [Presentation] Bilinear estimates and Nonlinear Klein-Gordon equations2011

    • Author(s)
      林仲夫
    • Organizer
      The 4th MSJ-SI Mathematical Society of Japan, Seasonal Institute
    • Place of Presentation
      九州大学
    • Year and Date
      2011-09-19
    • Related Report
      2010 Final Research Report
  • [Presentation] Bilinear estimates and Nonlinear Klein-Gordon equations2011

    • Author(s)
      林仲夫
    • Organizer
      The 4th MSJ-SI Mathematical Society of Japan, Seasonal Institute
    • Place of Presentation
      九州大学(招待講演)
    • Year and Date
      2011-09-19
    • Related Report
      2010 Annual Research Report
  • [Presentation] 双線形作用素の評価と非線形Klein-Gordon方程式への応用2011

    • Author(s)
      林仲夫
    • Organizer
      大阪市大・大阪府大合同「第2回南大阪応用数学セミナー」
    • Place of Presentation
      大阪市立大
    • Year and Date
      2011-07-02
    • Related Report
      2010 Final Research Report
  • [Presentation] 双線形作用素の評価と非線形Klein-Gordon方程式への応用2011

    • Author(s)
      林仲夫
    • Organizer
      大阪市大・大阪府大合同「第2回南大阪応用数学セミナー」
    • Place of Presentation
      大阪市立大学(招待講演)
    • Year and Date
      2011-07-02
    • Related Report
      2010 Annual Research Report
  • [Presentation] A bilinear estimate and its application to a quadratic nonlinear Klein-Gordon equation in two space dimensions2011

    • Author(s)
      林仲夫
    • Organizer
      阪大微分方程式セミナー
    • Place of Presentation
      大阪大学
    • Year and Date
      2011-05-27
    • Related Report
      2010 Annual Research Report 2010 Final Research Report
  • [Presentation] Nonexistence of scattering states for nonlinear dispersive equations2010

    • Author(s)
      林仲夫
    • Organizer
      偏微分方程式と数理物理学
    • Place of Presentation
      京都芝蘭会館
    • Year and Date
      2010-11-17
    • Related Report
      2010 Final Research Report
  • [Presentation] Nonexistence of scattering states for nonlinear dispersive equations2010

    • Author(s)
      林仲夫
    • Organizer
      偏微分方程式と数理物理学
    • Place of Presentation
      京都芝蘭会館(招待講演)
    • Year and Date
      2010-11-16
    • Related Report
      2010 Annual Research Report
  • [Presentation] Modified wave operator for a system of nonlinear Schrodinger equations2010

    • Author(s)
      林仲夫
    • Organizer
      「早稲田大学非線形偏微分方程式研究所」設立研究集会
    • Place of Presentation
      早稲田大学
    • Year and Date
      2010-11-10
    • Related Report
      2010 Final Research Report
  • [Presentation] Modified wave operator for a system of nonlinear Schrodinger equations2010

    • Author(s)
      林仲夫
    • Organizer
      「早稲田大学非線形偏微分方程式研究所」設立研究集会ワークショップ
    • Place of Presentation
      早稲田大学(招待講演)
    • Year and Date
      2010-11-10
    • Related Report
      2010 Annual Research Report
  • [Presentation] 非線形分散型方程式の散乱問題I,II2010

    • Author(s)
      林仲夫
    • Organizer
      「早稲田大学非線形偏微分方程式研究所」設立研究集会ミニコース
    • Place of Presentation
      早稲田大学(招待講演)
    • Year and Date
      2010-11-09
    • Related Report
      2010 Annual Research Report
  • [Presentation] Modified wave operator for a system of NLS equations in 2D2010

    • Author(s)
      林仲夫
    • Organizer
      Joint workshop on PDE at Jinhua
    • Place of Presentation
      Zhejiang Normal University(中国)
    • Year and Date
      2010-09-27
    • Related Report
      2010 Final Research Report
  • [Presentation] Modified wave operator for a system of NLS eguations in 2D2010

    • Author(s)
      林仲夫
    • Organizer
      Joint workshop on PDE at Jinhua
    • Place of Presentation
      Zhejiang Normal University(中国)(招待講演)
    • Year and Date
      2010-09-27
    • Related Report
      2010 Annual Research Report
  • [Presentation] Schrodinger方程式系の解の時間減衰評価2010

    • Author(s)
      李春花, 林仲夫
    • Organizer
      2010日本数学会秋季総合分科会
    • Place of Presentation
      名古屋大学
    • Year and Date
      2010-09-24
    • Related Report
      2010 Final Research Report
  • [Presentation] Schrodinger方程式系の解の時間減衰評価2010

    • Author(s)
      李春花, 林仲夫
    • Organizer
      日本数学会秋季総合分科会
    • Place of Presentation
      名古屋大学
    • Year and Date
      2010-09-24
    • Related Report
      2010 Annual Research Report
  • [Presentation] Time decay of solutions to a system of nonlinear Schrodinger equations2010

    • Author(s)
      林仲夫
    • Organizer
      第六回非線型の諸問
    • Place of Presentation
      山口大学
    • Year and Date
      2010-09-17
    • Related Report
      2010 Final Research Report
  • [Presentation] Time decay of solutions to a system of nonlinear Schrodinger equations2010

    • Author(s)
      林仲夫
    • Organizer
      第六回非線型の諸問題
    • Place of Presentation
      山口大学(招待講演)
    • Year and Date
      2010-09-16
    • Related Report
      2010 Annual Research Report
  • [Presentation] Asymptotic behavior of solutions to nonlinear Schrodinger equations2010

    • Author(s)
      林仲夫
    • Organizer
      The 35th Sapporo Symposium on Partial Differential Equations
    • Place of Presentation
      北海道大学
    • Year and Date
      2010-08-24
    • Related Report
      2010 Final Research Report
  • [Presentation] Asymptotic behavior of solutions to nonlinear Schrodinger equations2010

    • Author(s)
      林仲夫
    • Organizer
      The 35th Sapporo Symposium on Partial Differential Equations
    • Place of Presentation
      北海道大学(招待講演)
    • Year and Date
      2010-08-24
    • Related Report
      2010 Annual Research Report
  • [Presentation] On a system of nonlinear Schrodinger equations in 2d2010

    • Author(s)
      林仲夫
    • Organizer
      応用解析研究会
    • Place of Presentation
      早稲田大学
    • Year and Date
      2010-05-15
    • Related Report
      2010 Final Research Report
  • [Presentation] On a system of nonlinear Schrodinger equations in 2d2010

    • Author(s)
      林仲夫
    • Organizer
      応用解析研究会
    • Place of Presentation
      早稲田大学(招待講演)
    • Year and Date
      2010-05-15
    • Related Report
      2010 Annual Research Report
  • [Presentation] 非線形Schrodinger型方程式2009

    • Author(s)
      林仲夫
    • Organizer
      奈良女子大学数学談話会
    • Place of Presentation
      奈良女子大学
    • Year and Date
      2009-11-30
    • Related Report
      2010 Final Research Report
  • [Presentation] 空間2次元における2次の非線形クライン・ゴルドン方程式に対する波動作用素について2009

    • Author(s)
      林仲夫, P. Naumkin, 利根川聡
    • Organizer
      日本数学会秋季大会
    • Place of Presentation
      大阪大学
    • Year and Date
      2009-09-27
    • Related Report
      2010 Final Research Report
  • [Presentation] Dirac-Klein-Gordon方程式系の波動作用素2009

    • Author(s)
      池田正弘, 林仲夫
    • Organizer
      日本数学会秋季大会
    • Place of Presentation
      大阪大学
    • Year and Date
      2009-09-27
    • Related Report
      2010 Final Research Report
  • [Presentation] Direac-Klein-Gordon方程式系の波動作用素2009

    • Author(s)
      池田正弘, 林仲夫
    • Organizer
      日本数学会
    • Place of Presentation
      大阪大学
    • Year and Date
      2009-09-27
    • Related Report
      2009 Annual Research Report
  • [Presentation] 空間2次元における2次の非線形クライン・ゴルドン方程式に対する2009

    • Author(s)
      林仲夫, P.Naumkin, 利根川聡
    • Organizer
      日本数学会
    • Place of Presentation
      大阪大学
    • Year and Date
      2009-09-27
    • Related Report
      2009 Annual Research Report
  • [Presentation] 非線形Klein-Gordon方程式の散乱問題2009

    • Author(s)
      林仲夫
    • Organizer
      日本数学会,解析学賞受賞特別講演
    • Place of Presentation
      東京大学
    • Year and Date
      2009-03-28
    • Related Report
      2010 Final Research Report
  • [Presentation] 非線形 Klein-Gordon 方程式の散乱問題2009

    • Author(s)
      林仲夫
    • Organizer
      日本数学会, 解析学賞受賞特別講演
    • Place of Presentation
      東京大学
    • Year and Date
      2009-03-26
    • Related Report
      2009 Self-evaluation Report
  • [Presentation] Dirac-Klein-Gordon方程式の散乱問題について2009

    • Author(s)
      林仲夫
    • Organizer
      熊本大学応用解析セミナー
    • Place of Presentation
      熊本大学
    • Year and Date
      2009-01-30
    • Related Report
      2010 Final Research Report 2009 Annual Research Report
  • [Presentation] 非線形分散型方程式の漸近解析2009

    • Author(s)
      林仲夫
    • Organizer
      九州非線形偏微分方程式・九州冬の学校
    • Place of Presentation
      福岡大学
    • Related Report
      2010 Final Research Report
  • [Presentation] Dirac-Klein-Gordon方程式系の散乱問題2008

    • Author(s)
      B. E. W. Ratno, 林仲夫
    • Organizer
      日本数学会秋季大会
    • Place of Presentation
      東京工業大学
    • Year and Date
      2008-09-24
    • Related Report
      2010 Final Research Report
  • [Presentation] Dirac-Klein-Gordon方程式系の散乱問題2008

    • Author(s)
      B. E. W. Ratno 林 仲夫
    • Organizer
      日本数学会
    • Place of Presentation
      東京工業大学
    • Year and Date
      2008-09-24
    • Related Report
      2008 Annual Research Report
  • [Presentation] Dirac-Klein-Gordon方程式系の散乱問題2008

    • Author(s)
      林 仲夫
    • Organizer
      阪大微分方程式セミナー
    • Place of Presentation
      大阪大学
    • Year and Date
      2008-05-30
    • Related Report
      2008 Annual Research Report
  • [Presentation] 非線形Klein-Gordon方程式系の散乱問題2008

    • Author(s)
      林仲夫
    • Organizer
      Paris-Sud PDEセミナー
    • Place of Presentation
      パリ南大学(フランス)
    • Year and Date
      2008-03-11
    • Related Report
      2010 Final Research Report
  • [Presentation] Scattering problem for nonlinear Klein-Gordon equations2007

    • Author(s)
      Hayashi Nakao
    • Organizer
      International Conference on Applied Partial Differential Equations
    • Place of Presentation
      East Chaina Normal University, Shanghai, Chaina
    • Year and Date
      2007-07-05
    • Related Report
      2007 Annual Research Report

URL: 

Published: 2007-04-01   Modified: 2016-04-21  

Information User Guide FAQ News Terms of Use Attribution of KAKENHI

Powered by NII kakenhi