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Uniqueness of Solutions of Partial Differential Equations

Research Project

Project/Area Number 01540133
Research Category

Grant-in-Aid for General Scientific Research (C)

Allocation TypeSingle-year Grants
Research Field 解析学
Research InstitutionHyogo University of Teacher Education

Principal Investigator

WATANABE Kinji  Hyogo Univ. of Teacher Education, Assistant Professor, 学校教育学部, 助教授 (20004468)

Co-Investigator(Kenkyū-buntansha) MATSUYAMA Hiroshi  Hyogo Univ. of Teacher Education, Assistant professor, 学校教育学部, 助教授 (80028266)
YABUKI Haruichi  Hyogo Univ. of Teacher Education, Professor, 学校教育学部, 教授 (40027371)
NOMURA Yasunori  Hyogo Univ. of Teacher Education, Professor, 学校教育学部, 教授 (20029630)
ITAGAKI Yoshio  Hyogo Univ. of Teacher Education, Professor, 学校教育学部, 教授 (30006431)
YANAGIHARA Hiroshi  Hyogo Univ. of Teacher Education, Professor, 学校教育学部, 教授 (00033803)
小池 敏司  兵庫教育大学, 学校教育学部, 助教授 (60161832)
Project Period (FY) 1989 – 1990
Project Status Completed (Fiscal Year 1990)
Budget Amount *help
¥1,700,000 (Direct Cost: ¥1,700,000)
Fiscal Year 1990: ¥800,000 (Direct Cost: ¥800,000)
Fiscal Year 1989: ¥900,000 (Direct Cost: ¥900,000)
Keywordsparabolic equation / uniqueness / backward uniqueness / 方物型方程式
Research Abstract

In 1960, Lions and Malgrange have disputed on the backward uniqueness of the solutions of the parabolic equations and this problem is still open up to now. We completely solve it in case of the space dimension 1. That is, we give a sufficient condition for the backward uniqueness of the solutions of the parabolic equations associated with the realizations in L^2 (0.1) of the ordinary differential operators of order 2m under 2m boundary conditions. This result is published in the Journal of Mathematical Society of Japan.

Report

(3 results)
  • 1990 Annual Research Report   Final Research Report Summary
  • 1989 Annual Research Report
  • Research Products

    (20 results)

All Other

All Publications (20 results)

  • [Publications] 渡辺 金治: "Sur l′unicite retrograde dans les probleme mixted paraboligues;Cas de dimension 1" Journal of Mathematical Society of Japan. 42. 376-386 (1990)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1990 Final Research Report Summary
  • [Publications] 矢吹 治一: "Two classes of zeros of FaddeevーPopov deterninant" Nuclear Physics. 318. 464-482 (1989)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1990 Final Research Report Summary
  • [Publications] 小池 敏司: "Notes on C^O sufficiency of quasijets" Journal of Mathematical Society of Japan. 42. 266-275 (1990)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1990 Final Research Report Summary
  • [Publications] 松山 広: "A twisted version of the Frobinius ーSchur indicator and permutation reprensontations" 北海道数学雑誌. 495-508 (1990)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1990 Final Research Report Summary
  • [Publications] Eizaburo, Nagura: "School Surveys in the Early Modern Times" A Comprehensive Study of the Systematization of School in the End of the Edo and the Early Meiji Eras. 1. 1-27 (1989)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1990 Final Research Report Summary
  • [Publications] Sakae, Yoshioka: "School Administration of Ashikaga-han before and after the Meiji Restoration : With Reference to the Relation Between Ashikaga-gakko and hankos" A Comprehensive Study of the Systematization of School in the End of the Edo and the Early Meiji Eras. 2. (1990)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1990 Final Research Report Summary
  • [Publications] Kikuo, Takeshita: "The Reform of the School System of Shotokukan of Tottori-han and the Idea of the Reform : A Case Study of Kaei Reformation" A Comprehensive Study of the Systematization of School in the End of the Edo and the Early Meiji Eras. 2. (1990)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1990 Final Research Report Summary
  • [Publications] Yasuaki, Shin'ya: "The Systematization of School in Ogasawara-han in the early Meiji Era" A Comprehensive Study of the Systematization of School in the End of the Edo and the Early Meiji Eras. 2. (1990)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1990 Final Research Report Summary
  • [Publications] Yasumitsu, Kambe: "The Systematization of School of Mori-han in the End of the Edo and the Early Meiji Eras" A Comprehensive Study of the Systematization of School in the End of the Edo and the Early Meiji Eras. 1. 63-89 (1989)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1990 Final Research Report Summary
  • [Publications] Akihiko, Hashimoto: "The Enactment of the School Regulations by Dutch Medical Teachers in the Early Meiji Era : Focusing on the Regulations of Curricula and Examinations" A Comprehensive Study of the Systematization of School in the End of the Edo and the Early Meiji Eras. 1. 117-135 (1989)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1990 Final Research Report Summary
  • [Publications] 渡辺 金治: "Sur l′unicite^^′ re^^′trograde dans les proble^^`mes mixtes paraboligues;Cas ae dimension 1." Journal of Mathematical Societg of Japan. 42. 376-386 (1990)

    • Related Report
      1990 Annual Research Report
  • [Publications] 矢吹 治一: "Two classes of zeros of FaddeevーPopov determinant" Nuclear Physics. 318. 464-482 (1989)

    • Related Report
      1990 Annual Research Report
  • [Publications] 小池 敏司: "Notes on C^0 sufficiency of guasijets" Journal of Mathematical Society of Japan. 42. 266-275 (1990)

    • Related Report
      1990 Annual Research Report
  • [Publications] 松山 広: "A twisted version of the FrobeniusーSchur indicator and permutation representations" 北海道数学雑誌. 19. 495-508 (1990)

    • Related Report
      1990 Annual Research Report
  • [Publications] Kinji Watanabe: "Sur lunicite retrogradedans les problemes mixtes paraboliques; cas de dimension 1" Journal of Mathematical Society of Japan. 42. (1990)

    • Related Report
      1989 Annual Research Report
  • [Publications] Yasutoshi Nomura: "Rational points on elliptic curves I" Hyogo Univ. Teacher Ed.J.10. (1989)

    • Related Report
      1989 Annual Research Report
  • [Publications] Haruichi Yabuki: "Structure of the Gribov Horizon for the Non-Abelian Gauge Field Theory in Axial Gauge" Physics Letters. 231. 271-274 (1989)

    • Related Report
      1989 Annual Research Report
  • [Publications] S.Koike: "Notes on C^Oーsufficiency of quasi jets" J.of Math.Soc. Japan. 42. (1990)

    • Related Report
      1989 Annual Research Report
  • [Publications] Hiroshi Matsuyama: "A twisted version of the FrobeniusーSchur indicator and multiplicityーfree permutation representation" Hokkaido Math.Journal.

    • Related Report
      1989 Annual Research Report
  • [Publications] 板恒芳雄: "物理法則の統一的記述ー相対論の時間、空間像についての思考ー" 兵庫教育大学研究紀要. 10. (1990)

    • Related Report
      1989 Annual Research Report

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Published: 1989-04-01   Modified: 2016-04-21  

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