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Co-operative research of partial differential equations and its applications

Research Project

Project/Area Number 02302005
Research Category

Grant-in-Aid for Co-operative Research (A)

Allocation TypeSingle-year Grants
Research Field 解析学
Research InstitutionOsaka University

Principal Investigator

IKAWA Mitsuru  Osaka University Faculty of Sciences Professor, 理学部, 教授 (80028191)

Co-Investigator(Kenkyū-buntansha) ICHINOSE Takashi  Kanazawa University Faculty of Sciences Professor, 理学部, 教授 (20024044)
NAKAO Mitsuhiro  Kyushu University College of General Education Professor, 教養部, 教授 (10037278)
KURODA Sigetoshi  Gakushuin University Faculty of Sciences Professor, 理学部, 教授 (20011463)
FUJIWARA Daisuke  Tokyo Institute of Technology Faculty of Sciences Professor, 理学部, 教授 (10011561)
AGEMI Rentaro  Hokkaido University Faculty of Sciences Professor, 理学部, 教授 (10000845)
Project Period (FY) 1990 – 1991
Project Status Completed (Fiscal Year 1991)
Budget Amount *help
¥2,200,000 (Direct Cost: ¥2,200,000)
Fiscal Year 1991: ¥2,200,000 (Direct Cost: ¥2,200,000)
KeywordsElastic Equations / Scattering Theory / Spectrum / Hyperbolic Equations / Hypoellipticity / 双曲系方程式 / 多体問題 / 波動作用素 / エネルギ-の減衰 / 超局所解析 / 特異性の伝播 / 回折
Research Abstract

The subjects of this research were well achieved by meetings and discussions organized by each investigator and by a big meeting organized co-operatively by the whole investigators.
The subjects of this project are mainly concerned with theory of partial differential equations, but, as a matter of course, the theory of ordinary differential equations has deep relationships with studies of Partial differential equations. Therefore, we have organized the meetings in co-operations with researchers of ordinary differential equations. Thus, naturally the results obtained by this project extend over the whole theory of differential equations.
In the year of 1990, we organized mainly several middle size meetings, whose subjects were concentrated sharply in topics of central subjects of our project. Namely, we studied around Problems of hyperbolic equations, spectral and scattering theory, and elastic equation and hyperbolic problems appeared in engineering. In these meetings, very ardor discussions were exchanged and we have recognized the deep relations between different subjects. These meeting enable us to consider the various topics in partial differential equations in total. This permits us to treat the theory of partial differential equations as a non-separable subject, that is, in a global perspective of differential equations.
In 1991 we organized a big meeting which covers all the fields of differential equations. By these researches we have recognized the variety of the theory of differential equations and generated many germs which will certainly give us many beautiful fruits of mathematics.

Report

(3 results)
  • 1991 Annual Research Report   Final Research Report Summary
  • 1990 Annual Research Report
  • Research Products

    (24 results)

All Other

All Publications (24 results)

  • [Publications] 井川 満: "On scattering by obstacles" Proceeding of ICMーKyoto. 1145-1154 (1991)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1991 Final Research Report Summary
  • [Publications] 井川 満: "Singular perturbation of symbolic flows and poles of the zeta functions" Osaka J.Math.27. 281-300 (1990)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1991 Final Research Report Summary
  • [Publications] 藤原 大輔: "The stationary phase method with an estimate of the remainder term on a space of large dimension" Nagoya Math.J.124. 61-97 (1991)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1991 Final Research Report Summary
  • [Publications] 中尾 慎広: "Remarks on the existence and uniqueness of global decaying solutions of the nonーlinear dissipative wave equation" Math.Z.206. 265-276 (1991)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1991 Final Research Report Summary
  • [Publications] 中尾 慎広: "Existence of global smooth solutions to the initialーboundary value problem for the quasiーlinear wave equation with a degenerate dissipative term" J.Diff.Equations.

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1991 Final Research Report Summary
  • [Publications] 一瀬 孝: "Remarks on the Wyle quantized relativistic Hamiltonian" Note di Mathematica.

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1991 Final Research Report Summary
  • [Publications] IKAWA Mitsuru: "On scattering by obstacles" Proceeding of ICM-Kyoto. 1145-1154 (1991)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1991 Final Research Report Summary
  • [Publications] IKAWA Mitsuru: "Sigular perturbation of symbolic flows ad poles of the zeta function" Osaka J. Math.27. 281-300 (1990)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1991 Final Research Report Summary
  • [Publications] FUJIWARA Daisuke: "The Stationary phase method with and estimate of the remainder term on a space of large dimension" Nagoya Math. J.124. 61-67 (1991)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1991 Final Research Report Summary
  • [Publications] NAKAO Mitshiro: "Remarks on the existence and uniqueness of global decaying solutions of the non-linear dissipative wave equation" Math. Z.206. 265-276 (1991)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1991 Final Research Report Summary
  • [Publications] NAKAO Mitshiro: "Existence of global smooth solutions to the initial-boundary value problem for the quasi-linear wave equation with a degenerate dissipative term" J. Diff. Equations.

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1991 Final Research Report Summary
  • [Publications] ICHINOSE Takashi: "Remarks on the Wyle quantized relativestic Hamiltonian" Note di Mathematica.

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1991 Final Research Report Summary
  • [Publications] 井川 満: "On scattering by obstacles" Proceeding of ICMーKyoto,. 1145-1154 (1991)

    • Related Report
      1991 Annual Research Report
  • [Publications] 井川 満: "Singular perturbation of symboic flows and poles of the zeta functions" Osaka J.Math.27. 281-300 (1990)

    • Related Report
      1991 Annual Research Report
  • [Publications] 藤原 大輔: "The stationary phase method with an estimate of the remainer term on a space of large dimension" Nagoya Math.J.124. 61-97 (1991)

    • Related Report
      1991 Annual Research Report
  • [Publications] 中尾 愼宏: "Remarks on the existence and uniqueness of global decaying solurions of the nanlinear dissipative wave equation" Math.Z.206. 265-276 (1991)

    • Related Report
      1991 Annual Research Report
  • [Publications] 中尾 愼宏: "Existence of global smooth solutions to the initialーboemdy value problem for the quasiーlineas wave equation with a degenerote dissipatiue term" J.Diff.Equations.

    • Related Report
      1991 Annual Research Report
  • [Publications] 一瀬 孝: "Remarks on the Weyl quantized relativistic Hamiltonian" Note di Mathematica.

    • Related Report
      1991 Annual Research Report
  • [Publications] 井川 満: "On the existence of poles of the zeta functions for certain symbolic dynamics" Submitted to Osaka J.Math.

    • Related Report
      1990 Annual Research Report
  • [Publications] 井川 満: "On scattering by obstacles" to appear in Proceeding of ICMー90.

    • Related Report
      1990 Annual Research Report
  • [Publications] 藤原 大輔: "The Feyman path integral as an improper integral over the Sobolev space" Journees des equations aux derivees partielles,Saint JeanーdeーMonts. (1990)

    • Related Report
      1990 Annual Research Report
  • [Publications] 中尾 慎宏: "On solutions of the wave equation with a sublinear dissipative term II" Funk.Ekuac,. 33. 307-316 (1990)

    • Related Report
      1990 Annual Research Report
  • [Publications] 川下 美潮: "On the local energy decay property for the elastic wave equation with Neumann boundary condition" Submitted to Duke Math.J.

    • Related Report
      1990 Annual Research Report
  • [Publications] 谷島 賢二: "A remark on the longーrange scattering for Stark Hamiltonians"

    • Related Report
      1990 Annual Research Report

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Published: 1991-04-01   Modified: 2016-04-21  

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