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Mathematical analysis of nonlinear partial differential equations describing interaction of several fields

Research Project

Project/Area Number 21540190
Research Category

Grant-in-Aid for Scientific Research (C)

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

Principal Investigator

WADA Takeshi  熊本大学, 大学院・自然科学研究科, 准教授 (70294139)

Co-Investigator(Kenkyū-buntansha) NAKAMURA Makoto  東北大学, 大学院・理学研究科, 准教授 (70312634)
Project Period (FY) 2009 – 2011
Project Status Completed (Fiscal Year 2011)
Budget Amount *help
¥3,380,000 (Direct Cost: ¥2,600,000、Indirect Cost: ¥780,000)
Fiscal Year 2011: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2010: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2009: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Keywords非線形偏微分方程式 / 適切性 / 相互作用 / 函数方程式論 / 非線形Schrodinger方程式 / 分散型方程式 / 波動方程式
Research Abstract

We studied the well-posedness of nonlinear partial differential equations in mathematical physics and their systems. A given problem for a partial differential equation with initial or boundary conditions is called well-posed if the problem has a unique solution, and if the solution depends continuously on the data given in the problem. This is an important step to ensure that the equation correctly describes the phenomenon. In this research we proved the well-posedness of nonlinear Schrodinger equations and the Maxwell-Schrodinger system under appropriate conditions.

Report

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

    (17 results)

All 2012 2011 2010 2009 Other

All Journal Article (12 results) (of which Peer Reviewed: 12 results) Presentation (5 results)

  • [Journal Article] Continuous dependence for nonlinear Schrodinger equation in H^s2012

    • Author(s)
      H. Uchizono and T. Wada
    • Journal Title

      J. Math. Sci. Univ. Tokyo

      Volume: (印刷中)

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] On wellposedness for nonlinear Schrodinger equations with power nonlinearity in fractional order Sobolev spaces2012

    • Author(s)
      H. Uchizono and T. Wada
    • Journal Title

      J. Math. Anal. Appl

      Volume: (印刷中)

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Smoothing effects for Schrodinger equations with electromagnetic potentials and applications to the Maxwell-Schrodinger equations2012

    • Author(s)
      T. Wada
    • Journal Title

      J. Funct. Anal

      Volume: 263 Pages: 1-24

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Global solutions for nonlinear wave equations with localized dissipations in exterior domains2012

    • Author(s)
      M. Nakamura
    • Journal Title

      J. Differential Equations

      Volume: 252 Pages: 4742-4785

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Scattering theory for the Dirac Equation of Hartree type and the semirelativistic Hartree equation2012

    • Author(s)
      M. Nakamura and K. Tsutaya
    • Journal Title

      Nonlinear Anal. Series A : Theory, Methods and Applications

      Volume: 75 Pages: 3531-3542

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Smoothing effects for Schrodinger equations with electro-magnetic potentials and applications to the Maxwell-Schrodinger Equations2012

    • Author(s)
      Takeshi Wada
    • Journal Title

      Journal of Functional Analysis

      Volume: (印刷中) Issue: 1 Pages: 1-24

    • DOI

      10.1016/j.jfa.2012.04.010

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Scattering theory for the Dirac Equation of Hartree type and the semir elativistic Hartree equation2012

    • Author(s)
      Makoto Nakamura, Kimitoshi Tsutaya
    • Journal Title

      Nonlinear Analysis Series A : Theory, Methods and Applications

      Volume: 75 Pages: 3531-3542

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Small global solutions for nonlinear complex Ginzburg-Landau equations and nonlinear dissipative wave equations in Sobolev spaces2011

    • Author(s)
      M. Nakamura
    • Journal Title

      Rev. Math. Phys

      Volume: 23 Pages: 903-931

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Remarks on Keel-Smith-Sogge estimates and some applications to nonlinear higher-order wave equations2011

    • Author(s)
      M. Nakamura
    • Journal Title

      Differential Integral Equations

      Volume: 24 Pages: 519-540

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Small global solutions for nonlinear complex Ginzburg-Landau equations and nonlinear dissipative wave equations in Sobolev spaces2011

    • Author(s)
      Makoto Nakamura
    • Journal Title

      Reviews in Mathematical Physics

      Volume: 23 Pages: 903-931

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Global solutions for nonlinear wave equations with localized dissipations in exterior domains2011

    • Author(s)
      Makoto Nakamura
    • Journal Title

      Journal of Differential Equations

      Volume: 252 Pages: 4742-4785

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Remarks on Keel-Smith-Sogge estimates and some applications to nonlinear higher order wave equations

    • Author(s)
      Nakamura, Makota
    • Journal Title

      Differential and Integral Equations

      Volume: (未定 掲載確定)

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Presentation] 非線形Schrodinger方程式の解の初期条件に関する連続依存性について2011

    • Author(s)
      内園晴典, 和田健志
    • Organizer
      第125回日本数学会九州支部例会
    • Place of Presentation
      熊本大学
    • Year and Date
      2011-10-22
    • Related Report
      2011 Final Research Report
  • [Presentation] Smoothing effects for Schrodinger equations with electromagnetic potentials and applications to the Maxwell-Schrodinger Equations2011

    • Author(s)
      T. Wada
    • Organizer
      第7回非線型の諸問題
    • Place of Presentation
      熊本大学
    • Year and Date
      2011-09-25
    • Related Report
      2011 Final Research Report
  • [Presentation] Smoothing effects for Schrodinger equations with electro-magnetic potentials and applications to the Maxwell-Schrodinger Equations2011

    • Author(s)
      和田健志
    • Organizer
      非線型の諸問題
    • Place of Presentation
      熊本大学(招待講演)
    • Year and Date
      2011-09-24
    • Related Report
      2011 Annual Research Report
  • [Presentation] 電磁ポテンシャルを含むSchrodinger方程式の平滑化効果とMaxwell-Schrodinger方程式への応用2010

    • Author(s)
      和田健志
    • Organizer
      夏の偏微分方程式セミナー
    • Place of Presentation
      神戸大学瀧川記念会館
    • Year and Date
      2010-08-25
    • Related Report
      2011 Final Research Report
  • [Presentation] 空間2次元におけるMaxwell-Schrodinger方程式2009

    • Author(s)
      和田健志
    • Organizer
      夏の偏微分方程式セミナー
    • Place of Presentation
      龍谷大学セミナーハウスともいき荘(京都)
    • Year and Date
      2009-08-28
    • Related Report
      2011 Final Research Report

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

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