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Synthetic study on differential equations

Research Project

Project/Area Number 07304013
Research Category

Grant-in-Aid for Scientific Research (A)

Allocation TypeSingle-year Grants
Section総合
Research Field 解析学
Research InstitutionHOKKAIDO UNIVERSITY

Principal Investigator

AGEMI Rentaro  Hokkaido University, Graduate School of Science, Professor, 大学院・理学研究科, 教授 (10000845)

Co-Investigator(Kenkyū-buntansha) NAKAO Mitsuhiro  Kyusyu University, Graduate School of Mathematics, Professor., 大学院・数理学研究所, 教授 (10037278)
TAKANO Kyoichi  Kobe University, Faculty of Sciences, Professor, 理学部, 教授 (10011678)
ICHINOSE Takashi  Kanazawa University, Faculty of Sciences, Professor., 理学部, 教授 (20024044)
YAJIMA Kenji  University of Tokyo, Graduate Scool of Mathematical Sciences, Professor., 大学院・数理科学研究所, 教授 (80011758)
ISHII Hitoshi  Tokyo Metropolitan University, Faculty of Sciences, Professor., 理学部, 教授 (70102887)
岩崎 敷久  京都大学, 理学部, 教授 (70027374)
加藤 順二  東北大学, 理学部, 教授 (80004290)
Project Period (FY) 1995 – 1996
Project Status Completed (Fiscal Year 1996)
Budget Amount *help
¥15,500,000 (Direct Cost: ¥15,500,000)
Fiscal Year 1996: ¥6,900,000 (Direct Cost: ¥6,900,000)
Fiscal Year 1995: ¥8,600,000 (Direct Cost: ¥8,600,000)
Keywordsordinary differential equations / partial differential equations / elliptic differential equations / parabolic differential equations / hyperbolic differential equations / Fourier integral operators / existence of global solutions / blow-up of solutions / フーリェ積分作用素
Research Abstract

Head of this project held the meetings at Tokyo, July 1995 and at Sapporo, July 1996 and decided the schedules of conferences organized by investigators. In the conferences on differential equations held at Tokyo, December 1995 and 1996, there were approximately two hundred researchers from the whole country. The investigators also opened the fifteen local conferences, for example, The 20^<th> and 21^<st> Sapporo symposium on partial differential equations (Hokkaido Univ.), The analytic partial differential equations and related topics in ordinary differential equations (Nagoya Univ.), Symposium on nonlinear partial differential equations (Tokyo Metropolitan Univ.), etc. In the above conferences we obtained many significant research results in the following fields (see the report on this project in detail),
(1) The qualitive theory of ordinary differential equations,
(2) The local theory of partial differential equations
(3) The integral operators and elliptic equations
(4) The geometric theory of parabolic equations
(5) The global theory of evolution equations
(6) The nonlinear equations in theoritical physics

Report

(3 results)
  • 1996 Annual Research Report   Final Research Report Summary
  • 1995 Annual Research Report
  • Research Products

    (18 results)

All Other

All Publications (18 results)

  • [Publications] Kenji, Yajima: "Smoothness and non-smoothness of Fundamental solution of time dependent Schrodinger oquations" Comm. Marh. Phys.(in press).

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] Takashi, Ichinose: "Estemate of the difference between the Kac operator and Schrodiger semigroup" Comm. Marh. Phys.(in press).

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] Rentaro, Agemi: "The null condition and global existence of solutions to systems of wave equations with different speeds" Series on Advance in Mathematics for Applied Sciences. (in press). (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] Hitoshi, Ishii: "Degenerate parobolic. PDEs with discontinuities and general evalutions of surface" Advance Differential equations. 1. 51-72 (1996)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] Kyoichi, Takano: "A normal form of Hamiltonian systems of several time variables with a regular sungurality" J. Diff. Eqs.127. 337-364 (1996)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] Mitsuhiro, Nakao: "Decay of solutions of the wave equation with a local nonlinear dissipation" Math. Ann.305. 403-417 (1966)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] Kenji Yajima: "Smoothness and non-smoothness of the fundamental solution of time dependent Schrodinger equations" Comm.Math.Phys. (In press). (1996)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] Takashi Ichinose (with S.Takanobu): "Estimate of the differences between the Kac operator and the Schrodinger semigroup" Comm.Math.Phys. (In press). (1996)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] Rentaro Agemi (with K.Yokoyama): "The null condition and global existence of solutions to systems of were wave equations with different speeds" Series on Advances in Mathematics for applied Science. (In press).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] Hitoshi Ishii: "Degenerated parabolic PDEs with discontinuities and general evolutions of surface" Advance Differential equation. 1. 51-72 (1996)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] Kyoichi Takano (with H.Kimura and A.Matsumiya): "A normal form of Hamiltonian systemsof several time variables with a regular singularity" J.Diff.Eqs.127. 337-364 (1996)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] Mitsuhiro Nakao: "Decay of solutions of the wave equation with a local nonlinear dissipation" Math.Ann.305. 403-417 (1996)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] Kenji, Yajima: "Smoothness and non-smoothness of fundamental solution of time dependent Schrodinger equations" Comm. Math. Phys.(in press).

    • Related Report
      1996 Annual Research Report
  • [Publications] Takashi, Ichinose: "Estemate of the difference between the Kac operator and Schrodinger semigroup" Comm. Math. Phys.(in press).

    • Related Report
      1996 Annual Research Report
  • [Publications] Rentaro, Agemi: "The null condition and global existence of solutions to systems of wave equations with different speeds" Series on Advance in Mathematics for Applied Sciences. (in press). (1997)

    • Related Report
      1996 Annual Research Report
  • [Publications] Hitoshi, Ishii: "Degenerate pavobolic. PDEs with discontinuities and general evolutions of surface" Advance Differential equations. 1. 51-72 (1996)

    • Related Report
      1996 Annual Research Report
  • [Publications] Kyoichi, Takano: "A normal form of Hamiltonian systems of several time variables with a regular singurality" J. Diff. Eqs.127. 337-364 (1966)

    • Related Report
      1996 Annual Research Report
  • [Publications] Mitsuhiro, Nakao: "Decay of solutions of the wave equation with a local nonlinear dissepation" Math. Ann.305. 403-417 (1966)

    • Related Report
      1996 Annual Research Report

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Published: 1995-04-01   Modified: 2016-04-21  

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