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Inverse scattering problems for Dirac equations

Research Project

Project/Area Number 09640182
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field 解析学
Research InstitutionEhime University (1998)
Kyoto University (1997)

Principal Investigator

ITO Hiroshi  Ehime University, Fuculty of Engineering, Assistant Professor, 工学部, 助教授 (90243005)

Co-Investigator(Kenkyū-buntansha) SHIMADA Shinichi  Setsunan University, Fuculty of Engineering, Assistant Professor, 工学部, 助教授 (40196481)
OKAJI Takashi  Kyoto University, Graduate School of Science, Assistant Professor, 大学院理学研究科, 助教授 (20160426)
IWATSUKA Akira  Kyoto Institute of Technology, Faculty of Textile of Science, Professor, 繊維学部, 教授 (40184890)
IGARI Katsujyu  Ehime University, Fuculty of Engineering, Professor, 工学部, 教授 (90025487)
SADAMATSU Takashi  Ehime University, Fuculty of Engineering, Professor, 工学部, 教授 (10025439)
池部 晃生  摂南大学, 工学部, 教授 (00025280)
土居 伸一  京都大学, 大学院・理学研究科, 助手 (00243006)
Project Period (FY) 1997 – 1998
Project Status Completed (Fiscal Year 1998)
Budget Amount *help
¥3,100,000 (Direct Cost: ¥3,100,000)
Fiscal Year 1998: ¥1,100,000 (Direct Cost: ¥1,100,000)
Fiscal Year 1997: ¥2,000,000 (Direct Cost: ¥2,000,000)
KeywordsDirac equation / scattering operator / scattering theory / inverse scattering theory / relativistic quantum mechanics / relativistic Schrodinger equation / 相対論的不変性
Research Abstract

We have considered an inverse scattering problem for Dirac equations with a time-dependent electromagnetic field. In this work it has been shown that some part of the electromagnetic field can be reconstructed from the scattering operator. Moreover, we have shown that the field can be completely reconstructed if the field is time-independent or satisfies some exponential decay condition. Our assumptions and results are independent of a choice of inertial frames, which is important for the relativistic theory. We have also shown that a similar result holds for a relativistic Schrodinger equation. The study for Schrodinger and Pauli equations is important for that of Dirac equations. Iwatsuka has studied the asymptotic distribution of eigenvalues for Pauli operators with Hideo Tamura. Okaji has shown, with De Carli, that the strong unique continuation property holds for Dirac operators with scalar potentials. Shimada has investigated Schrodinger equations with a potential supported in a line. Igari has studied the propagation of the singularities of a solution for some Cauchy problem in a complex domain. Sadamatsu has obtained a necessary condition for the well-posedness for initial value problems for some degenerate parabolic equations.

Report

(3 results)
  • 1998 Annual Research Report   Final Research Report Summary
  • 1997 Annual Research Report
  • Research Products

    (34 results)

All Other

All Publications (34 results)

  • [Publications] Hiroshi Ito: "An inverse scattering problem for Dirac equations with time-dependent electromagnetic potentials" Pub.RIMS, Kyoto Univ.34・4. 355-381 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Hiroshi Ito: "A time-dependent method for inverse scattering problems" 京都大学数理解析研究所講究録. 1036. 46-64 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] 伊藤 宏: "Inverse scattering problems for Dirac operators with time-dependent electromagnetic potentials" 京都大学数理解析研究所講究録. 1047. 26-35 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Katsuju Igari: "Propagation of singularities in the ramlfied Cauchy problem for a class of operators with non-involutive multiple characteristics" Pub.RIMS, Kyoto Univ.-. 35・2(発行予定).

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Akira Iwatsuka: "asymptotic distribution of eigenvalves for Pauli operators with spherically symmetric magnetic fields" Tsukuba Journal of Mathematics. 22・2. 281-303 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Akira Iwatsuka: "asymptotic distribution of eigenvalves for Pauli operators with non constant magnetic fields" Duke Mathematical Journal. 93・3. 535-574 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Akira Iwatsuka: "Asymptotic distribution of negative eigenvalves for two dimensional Pavli operators with nonconstant magnetic fields" Annales de I'Institut Fourier. 48・2. 479-515 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] 大鍛治 隆司: "対称構造と偏微分方程式の解の特異性の伝播" 京都大学数理解析研究所講究録. 1056. 75-96 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Takashi Okaji: "Uniqueness of the Cacchy problem for elliptic operators with fourfold characteristic of constant multiplicity" Comm.P.D., Eqs.,. 22・182. 269-305 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] 島田伸一: "A solvable model for line interaction" 京都大学数理解析研究所講究録. 994. 168-183 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Hiroshi T.Ito: "An inverse scattering problem for Dirac equations with time-dependent lectromagnetic potentials" Pub.R.I.M.S, Kyoto Univ.34. 355-381 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Hiroshi Ito: "A time-dependent method for inverse scattering problems" RIMS Kokyuroku. 1036. 46-64 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Hiroshi Ito: "Inverse scattering problems for Dirac operators with time-dependent electromagnetic potentials(in Japanese)" RIMS Kokyuroku. 1047. 26-35 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Ktsuji Igari: "Propagation of singularities in the ramified Cauchy Problem for a class of operators with non-involutive multiple characteristics" to appear in Publ.R.I.M.S., Kyoto Univ.35 (2). (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Akira Iwatsuka: "Asymptotic distribution of eigenvalues for Pauli operators with spherically symmetric magnetic fields" Tsukuba Journal of Mathematics. 22-2. 281-303 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Akira Iwatsuka: "Asymptotic distribution of eigenvalues for Pauli Operators with nonconstant magnetic fields" Duke Mathematical Journal. 93-3. 535-574 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Akira Iwatsuka: "Asymptotic distribution of negative eigenvalues for two dimensional Pauli operators with nonconstant magnetic fields" Annales de l'Institut Fourier. 48-2. 479-515 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Takashi Okaji: "Taishoukouzou to henbibunhouteisiki no kai no tokuisei no denpa (in Japanese)" RIMS Kokyuroku. 1056. 75-96 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Takashi Okaji: "Uniqueness of the Cauchy problem for elliptic operators with fourfold characteristics of constant multiplicity" Comm.P.D., E qs.22-1 & 2. 269-305 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Shinichi Shimada: "A solvable model for line interaction (in Japanese)" RIMS Kokyuroku. 994. 168-183 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Hiroshi Ito: "An inversescattering problem for Dirac equations with time-dependent electromagnetic potentials" Pub.RIMS.,Kyoto Univ.34・. 355-381 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] Hiroshi Ito: "A time-dependent method for inverse scattering problems" 京都大学数理解析研究所講究録. 1036. 46-64 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] 伊藤宏: "Inverse scattering problems for Dirac operators with time-dependent electromagnetic potentials" 京都大学数理解析研究所講究録. 1047. 26-35 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] Katsuju Igari: "Propagation of Singularities in the ramified Cauchy problem for a class of operators with non-involutive multiple characteristics" Pub.RIMS.,Kyoto Univ.35・2発行予定.

    • Related Report
      1998 Annual Research Report
  • [Publications] Akira Iwatsuka: "Asymptotic distribution of eigenvalues for Pauli operators with spherically symmetric magnetic fields" Tsukuba Journal of Mathematics. 22-2. 281-303 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] Akira Iwatsuka: "Asymptotic distribution of eigenvalues for Pauli operators with nonconstant magnetic fields" Duke Mathematical Journal. 93-3. 535-574 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] Akira Iwatsuka: "Asymptotic distribution of negative eigenvalues for two dimensional Pauli operators with nonconstant magnetic fields" Annales de l'Institut Fourier. 48・2. 479-515 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] 大鍛冶 隆司: "対称構造と偏微分方程式の解の特異性の伝播" 京都大学数理解析研究所講究録. 1056. 75-96 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] Hiroshi Ito: "A time-dependent method for inverse scattering problems" 数理研講究録. 1036(発行予定).

    • Related Report
      1997 Annual Research Report
  • [Publications] Akira Iwatsuka: "Asymptotic distribution of eigenvalves for Pauli operators with spherically synmetric magnetic fields" Tsukuba Math J.(発行予定).

    • Related Report
      1997 Annual Research Report
  • [Publications] Akira Iwatsuka: "Asymptotic distribution of eigenvalves for Pauli operators with nomconstant magnetic fields" Duke Mathematical Journal. (発行予定).

    • Related Report
      1997 Annual Research Report
  • [Publications] Akira Iwatsuka: "Asymptotic distribution of negative eigenvalves for two dimensicnal Pauli operators with noncanstant magnetic fields" Annales de l´Institut Fourier. (発行予定).

    • Related Report
      1997 Annual Research Report
  • [Publications] Takashi Okaji: "Uniqueness of the Cauchy problem for elliptic operators with fourfold chayacteristics of constant moltiplicity" Comm. P. D. E8s.22. 269-305 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] 島田,伸一: "A solvable model for lime interaction" 数理研講究録. 994. 168-183 (1997)

    • Related Report
      1997 Annual Research Report

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Published: 1997-04-01   Modified: 2016-04-21  

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