• Search Research Projects
  • Search Researchers
  • How to Use
  1. Back to previous page

A study of solutions of systems of higher order partial differential equations by algebraic analysis methods and formula manipulation methods

Research Project

Project/Area Number 26400110
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Basic analysis
Research InstitutionThe University of Tokyo

Principal Investigator

Kataoka Kiyoomi  東京大学, 大学院数理科学研究科, 名誉教授 (60107688)

Project Period (FY) 2014-04-01 – 2018-03-31
Project Status Completed (Fiscal Year 2017)
Budget Amount *help
¥3,120,000 (Direct Cost: ¥2,400,000、Indirect Cost: ¥720,000)
Fiscal Year 2016: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2015: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2014: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Keywords解析関数 / 偏微分方程式系 / 初期値・境界値混合問題 / D-加群 / 佐藤超関数 / 層のマイクロ台 / 一般化固有関数 / 蔵本モデル / 蔵本予想 / 共鳴現象 / 非線形発展方程式 / 一般化固有値 / 解析性 / 分布関数 / ヒルベルト空間 / レゾルベント / ガウス分布 / 共鳴極 / 漸近展開 / 初期値境界値混合問題 / 超局所解析 / 回折現象 / Lopatinskii条件 / マイクロ台 / 円の族を含む曲面 / 5階偏微分方程式系 / 非線形偏微分方程式系 / 数式処理 / 境界値問題 / 代数解析
Outline of Final Research Achievements

Concerning systems of linear analytic partial differential equations, we succeeded in giving coordinate-free formulations of the initial-boundary value mixed problems for D_X modules. At the same time we obtained a key theorem on the estimate of micro-supports of some holomorphic solution sheaf complexes in the sense of M.Kashiwara-P.Schapira, which is an essential tool clarifying the propagation of micro-analyticity of Sato hyperfunction solutions along the boundary. Concerning non-linear differential equations, we succeeded in clarifying the generalized eigenfunction expansions due to Hayato Chiba's theory on Kuramoto's weakly coupled many oscillators model on a circle for resonance phenomena. We found some essential error in Chiba's theory and gave a correct formulation and a proof.

Report

(5 results)
  • 2017 Annual Research Report   Final Research Report ( PDF )
  • 2016 Research-status Report
  • 2015 Research-status Report
  • 2014 Research-status Report
  • Research Products

    (11 results)

All 2018 2017 2016 2015 2014

All Journal Article (3 results) (of which Peer Reviewed: 2 results,  Open Access: 3 results) Presentation (7 results) (of which Int'l Joint Research: 3 results,  Invited: 5 results) Book (1 results)

  • [Journal Article] The functor $\beta_Y(\cdot)$ and mixed problems for ${\mathcal D}_X$-modules2016

    • Author(s)
      Kiyoomi Kataoka
    • Journal Title

      京都大学数理解析研究所講究録別冊

      Volume: B61

    • Related Report
      2016 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] Sato Hyperfunctions and Reproducing Kernels2016

    • Author(s)
      片岡 清臣
    • Journal Title

      京都大学数理解析研究所講究録

      Volume: 1980 Pages: 125-138

    • Related Report
      2015 Research-status Report
    • Open Access
  • [Journal Article] A review of the results on second analytic singularities in diffraction problems2016

    • Author(s)
      Kiyoomi Kataoka
    • Journal Title

      京都大学数理解析研究所講究録別冊

      Volume: B57 Pages: 159-174

    • Related Report
      2015 Research-status Report
    • Peer Reviewed / Open Access
  • [Presentation] 蔵本予想に関連する作用素の一般化固有値について2018

    • Author(s)
      片岡清臣
    • Organizer
      日本数学会年会
    • Related Report
      2017 Annual Research Report
  • [Presentation] Some remarks on Hayato Chiba's theory about Kuramoto conjecture2017

    • Author(s)
      片岡清臣
    • Organizer
      京都大学RIMS共同研究 「Microlocal analysis and asymptotic analysis」
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Sobolev forms for microfunctions with real analytic parameters and the microlocal energy method2016

    • Author(s)
      Kiyoomi Kataoka
    • Organizer
      京都大学RIMS 共同研究 「超局所解析と特異摂動論の新展開 」
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2016-10-03
    • Related Report
      2016 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] 佐藤超関数と再生核形式2015

    • Author(s)
      片岡 清臣
    • Organizer
      京都大学数理解析研究所共同研究「再生核の応用についての総合的な研究」
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2015-10-07
    • Related Report
      2015 Research-status Report
    • Invited
  • [Presentation] The functor B_Y( . ) and mixed problems for D_X-modules2015

    • Author(s)
      Kiyoomi Kataoka
    • Organizer
      京都大学数理解析研究所共同研究「Microlocal Analysis and Singular Perturbation Theory 」
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2015-10-05
    • Related Report
      2015 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] 実解析的パラメーターをもつ佐藤超関数に対するソボレフ型2次形式とその応用2015

    • Author(s)
      片岡 清臣,山崎 海斗
    • Organizer
      日本数学会秋季総合分科会函数解析学分科会
    • Place of Presentation
      京都産業大学
    • Year and Date
      2015-09-13
    • Related Report
      2015 Research-status Report
  • [Presentation] A review of the results on second analytic singularities in diffraction problems, and some geometric proofs2014

    • Author(s)
      片岡 清臣
    • Organizer
      京都大学RIMS 共同研究「超局所解析の諸相」(研究代表者: 本多尚文(北大))
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2014-10-20 – 2014-10-24
    • Related Report
      2014 Research-status Report
    • Invited
  • [Book] 数学の現在 e2016

    • Author(s)
      片岡清臣(斎藤毅(東大数理)編集)
    • Publisher
      東京大学出版会
    • Related Report
      2016 Research-status Report

URL: 

Published: 2014-04-04   Modified: 2019-03-29  

Information User Guide FAQ News Terms of Use Attribution of KAKENHI

Powered by NII kakenhi