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Inverse Problems in Nonlinear Phenomena

Research Project

Project/Area Number 15540201
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Global analysis
Research InstitutionTokyo University of Marine Science and Technology (2004-2006)
東京水産大学 (2003)

Principal Investigator

KAMIMURA Yutaka  Tokyo University of Marine Science and Technology, Faculty of Marine Science, Professor, 海洋科学部, 教授 (50134854)

Co-Investigator(Kenkyū-buntansha) IWASAKI Katsunori  Tokyo University of Marine Science and Technology, Faculty of Mathematics, Professor, 大学数理学研究院, 教授 (00176538)
TSUBOI Kenji  Tokyo University of Marine Science and Technology, Faculty of Marine Science, Professor, 海洋科学部, 教授 (50180047)
NAKASHIMA Kimie  Tokyo University of Marine Science and Technology, Faculty of Marine Science, Associate Professor, 海洋科学部, 助教授 (10318800)
Project Period (FY) 2003 – 2006
Project Status Completed (Fiscal Year 2006)
Budget Amount *help
¥3,100,000 (Direct Cost: ¥3,100,000)
Fiscal Year 2006: ¥800,000 (Direct Cost: ¥800,000)
Fiscal Year 2005: ¥800,000 (Direct Cost: ¥800,000)
Fiscal Year 2004: ¥700,000 (Direct Cost: ¥700,000)
Fiscal Year 2003: ¥800,000 (Direct Cost: ¥800,000)
Keywordsenergy dependent scattering / inverse scattering problem / inverse problem / Schrodinger equation / Marchenko equation / potentials / 移流拡散方程式 / 再構成法 / マルチェンコ方程式 / シュレディンガー方程式 / クライン・ゴードン方程式 / 非線形問題 / Marchenkoの方程式 / カオス / 周期軌道 / モデル方程式 / 生物個体数
Research Abstract

This research was intended to make a scheme for determination of the nonlinearities and/or governed equations in nonlinear problems from a viewpoint of inverse problems. Main results are as follows :
1.An inverse problem to determine an unknown velocity in two-dimensional, time-independent advection-diffusion equation from data observed at a depth-level was discussed. A procedure by which the velocity is reconstructed from the observed data is established and, as a consequence, the uniqueness of the velocity realizing the prescribed data was proved.
2.Related with the problem in (1), an inverse scattering problem to recover the potentials of an energy dependent Schrodinger equation from the scattering data was discussed. A new inversion formula was developed, by which the potentials are recovered directly through the solution of a Marchenko equation. By means of this inverse formula, a necessary and sufficient condition for a given function to be the scattering data was obtained.

Report

(5 results)
  • 2006 Annual Research Report   Final Research Report Summary
  • 2005 Annual Research Report
  • 2004 Annual Research Report
  • 2003 Annual Research Report
  • Research Products

    (20 results)

All 2007 2006 2005 2004 Other

All Journal Article (17 results) Book (1 results) Publications (2 results)

  • [Journal Article] An inversion formula in energy dependent scattering2007

    • Author(s)
      Yutaka Kamimura
    • Journal Title

      Journal of Integral Equations and Applications (in press)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Energy dependent inverse scattering2007

    • Author(s)
      Yutaka Kamimura
    • Journal Title

      Funkcioj Ekvacioj (in press)

    • NAID

      130000140706

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] An inverse problem in advection-diffusion2007

    • Author(s)
      Yutaka Kamimura
    • Journal Title

      Journal of Physics, Conference Series (in press)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] エネルギー依存逆散乱理論2007

    • Author(s)
      上村 豊
    • Journal Title

      京都大学数理解析研究所講究録 (印刷中)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] An inversion formula in energy dependent scattering2007

    • Author(s)
      Yutaka Kamimura
    • Journal Title

      Journal of Integral Equations and Application in press (proof)

      Pages: 40-40

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Energy dependent inverse scattering2007

    • Author(s)
      Yutaka Kamimura
    • Journal Title

      Funkcioj Ekvacioj in press (preprint)

      Pages: 24-24

    • NAID

      130000140706

    • Related Report
      2006 Annual Research Report
  • [Journal Article] An inverse problem in advection-diffusion2007

    • Author(s)
      Yutaka Kamimura
    • Journal Title

      Journal of Physics. Conference Series in press (preprint)

      Pages: 20-20

    • Related Report
      2006 Annual Research Report
  • [Journal Article] エネルギー依存逆散乱理論2007

    • Author(s)
      上村 豊
    • Journal Title

      京都大学数理解析研究所講究録 印刷中(ゲラ刷)

      Pages: 7-7

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Reconstruction of a current from tracer observation and the inverse problem2006

    • Author(s)
      上村 豊
    • Journal Title

      京都大学数理解析研究所講究録 1474

      Pages: 76-83

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Reconstruction of a current from tracer observation and inverse problem2006

    • Author(s)
      Yutaka Kamimura
    • Journal Title

      RIMS Kokyuroku 1474

      Pages: 76-83

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Reconstruction of a Current from Tracer Observation and the Inverse Scatterring2006

    • Author(s)
      Yutaka Kamimura
    • Journal Title

      数理解析研究所講究録 (印刷中)

    • Related Report
      2005 Annual Research Report
  • [Journal Article] 流れの再構成の数学的方法2005

    • Author(s)
      上村 豊
    • Journal Title

      数理水産科学 3

      Pages: 2-14

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary 2005 Annual Research Report
  • [Journal Article] A mathematical method in reconstruction of a current2005

    • Author(s)
      Yutaka Kamimura
    • Journal Title

      Suuri Suisan Kagaku 3

      Pages: 2-14

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] An inversion formula in energy dependent scattering

    • Author(s)
      Yutaka Kamimura
    • Journal Title

      Journal of Integral Equations and applications (in press)

      Pages: 40-40

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Energy dependent inverse scattering

    • Author(s)
      Yutaka Kamimura
    • Journal Title

      Funkcioj Ekvacioj (in press)

      Pages: 24-24

    • NAID

      130000140706

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] An inverse problem in advection-diffusion

    • Author(s)
      Yutaka Kamimura
    • Journal Title

      Journal of Physics, Conference Series (in press)

      Pages: 20-20

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Energy dependent inverse scattering theory

    • Author(s)
      Yutaka Kamimura
    • Journal Title

      RIMS Kokyuroku (in press)

      Pages: 7-7

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Book] 数学セミナー2月号 特集 積分方程式、逆問題との交差2004

    • Author(s)
      上村 豊
    • Publisher
      日本評論社
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Publications] 上村 豊: "逆問題との交差"数学セミナー. 43 no2. 21-25 (2004)

    • Related Report
      2003 Annual Research Report
  • [Publications] K.Nakashima: "Multi-layered stationary solutions for a spatially inhomogeneous Allen-Cahn equation"Journal of Differential equations. 191. 234-276 (2003)

    • Related Report
      2003 Annual Research Report

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Published: 2003-04-01   Modified: 2016-04-21  

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