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Solutions of Differential Equations and Applications

Research Project

Project/Area Number 06302012
Research Category

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

Allocation TypeSingle-year Grants
Research Field 解析学
Research InstitutionTokyo Metropolitan University

Principal Investigator

MOCHIZUKI Kiyoshi  Tokyo Metropolitan Univ., 理学部, 教授 (80026773)

Co-Investigator(Kenkyū-buntansha) ICHINOSE Takashi  Kanazawa University, 理学部, 教授 (20024044)
UKAI Seiji  Tokyo Inst.of Technology, 情報理工学研究科, 教授 (30047170)
KAJITANI Kunihiko  Univ.of Tsukuba, 数学系, 教授 (00026262)
KATO Junji  Tohoku Univ., 理学研究科, 教授 (80004290)
KURATA Kazuhiro  Tokyo Metropolitan Univ., 理学部, 助教授 (10186489)
Project Period (FY) 1994 – 1995
Project Status Completed (Fiscal Year 1995)
Budget Amount *help
¥11,200,000 (Direct Cost: ¥11,200,000)
Fiscal Year 1995: ¥5,400,000 (Direct Cost: ¥5,400,000)
Fiscal Year 1994: ¥5,800,000 (Direct Cost: ¥5,800,000)
Keywordsdifferential equations / applied mathematics / numerical analysis / plasma physics / fluid mechanics / quantum mechanics / 量子論 / 非線形発展方程式 / 経路積分 / 波動方程式 / 逆問題 / 符号理論 / 数理物理 / 作用素論 / 非線形拡散方程式
Research Abstract

The study of differential equations extends in various directions. Among them we, the investigators of this project, have mainly concerned with the problems related Physics, Engineering and other applied sciences. To develop mathematical researches in these fields, we need joint studies with many related investigators. We made plan and managed several symposiums under the following three principles ;
1. To proceed cooperations with investigotors of Applied mathematics, Applied Physics, Numerical Analysis and Information Science.
2. To recomend young mathematician, especially graduate students, to participate in the symposium and to give lectires.
3. To cell to foreign investigators who are visiting Japan to participate in the symposium.
We actually or ganized morethan 20 symposiums in these two years. In each of them we could invite investigators of the related fields cited above. Moreover, among 300 lectures anounced in these symposiums, morethan 30 lectures are given by graduate students and also 30 lectures are given by foreign investigators.
These plan brought us fruitfull results, and this project is executed successfully. Details are sumonarized in the 「Report of Research Results」 of this project.

Report

(3 results)
  • 1995 Annual Research Report   Final Research Report Summary
  • 1994 Annual Research Report
  • Research Products

    (30 results)

All Other

All Publications (30 results)

  • [Publications] K. Mochizuki, R.Suzuki: "Critical exponent and critical blow-up for quasilinear parabolic equations" Isreal Journal Mathematics. (In press).

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] K. Kurata: "Local boundedness and continutity for weak solutions of -(v-ib)^2u+Vu=0" Mathematishe Zaitschrift. (To ppprer).

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] J. Kato: "Stability property and phase space" Rockey Mountain Journal Mathematics. 25. 315-338 (1995)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] K. Kajitani, A. Baba: "The Cauchy problem for Schrodinger type equations" Bull. Sci. Math.119. 459-473 (1995)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] S. Ukai, T. Makino: "Local smooth solutions of the relativistic Euler equations" Journal Math. Kyoto University. 35. 105-111 (1995)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] T. Ichinose: "Some results on the relativistic Hamiltonian: Selfadjointness and imaginary time path integrals" Diff. Equations Math Phys. International Press. 116-130 (1995)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] K.Asano: "Examples of statinary Euler flows" Acta Applicadae Mathematics. 37. 13-20 (1994)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] Y.Kametaka: "On periodic binomial coefficients(in press)" Proc. 2-nd Russia-Japan seminar.

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] K.Mochizuki, R.Suzuki: "Critical bxponent and critical blow-up for quasilinear parablic equations" Israel J.Math. (in press).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] K.Kurata: "Local bounded ness and continuity for weak solutions of -(V-ib)^2u+Vu=0" Math.Z.(to appear).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] J.Kato: "Stability property and phase space" Rockey Mountain J.Math. 25. 315-338 (1995)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] K.Kajitani, A.Baba: "The Cauchy problem for Schrodinger tyhpe equations" Bul.Sci.Math. 119. 459-473 (1995)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] S.Ukai, T.Makino: "Local smooth solutions of the relativistic Euler equations" J.Math.Kyoto U.35. 105-111 (1995)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] T.Ichinose: "Someremarks on the relatiuistic Hamiltonian : Selfadjointness and imaginarytime path integrals" Diff.Eqo.Math, Phys.International press. 116-130 (1995)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] K.Asano: "Examples of stationary Euler flows" Acta Applicadae Math.37. 13-20 (1994)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] Y.Kametaka: "On periodic binomial coefficients" Proc.2-nd Russia-Japan seminor. (in press).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] Kiyoshi Mochizuki and Ryuichi Suzuki: "Critical exponent and critical klow-up for quauilinear parabolic equations" Israel Joarnal Mathematies. (To appear).

    • Related Report
      1995 Annual Research Report
  • [Publications] Kazuhiro Kurata: "Local boundedness and continuity for weak solutions of-(V-ib)^2u+Vu=0" Mathematishe Zautschrift. (To appear).

    • Related Report
      1995 Annual Research Report
  • [Publications] Junji Kato: "Stakility property and phase space" Rockey Mountain Journal of Mathematics. 25. 315-338 (1995)

    • Related Report
      1995 Annual Research Report
  • [Publications] Kunihiko Kajitani and A.Baba: "The Cauchy problem for Schroclinger type equations" Bull.Sci.Math.119. 459-473 (1995)

    • Related Report
      1995 Annual Research Report
  • [Publications] Seiji Ukai and Tetsu Makino: "Local smooth solutions of the relativistic Euler equations" Journal Math Kyoto University. 35. 105-111 (1995)

    • Related Report
      1995 Annual Research Report
  • [Publications] Takashi Ichinose: "Some resualts on the relativistic Hamiltonian:Selfadjointness and imaginary-time path integral" Diff.Equations Math.Phys.International press. 116-130 (1995)

    • Related Report
      1995 Annual Research Report
  • [Publications] Kiyoshi Asano: "Example of Stationary Euler flows" Acta Applicandal Mathematics. 37. 13-20 (1994)

    • Related Report
      1995 Annual Research Report
  • [Publications] Yoshinori Kametaka: "On periodic binomial coefficients(In press)" Proc.2-nd.Russia-Japan seminar on integral egs in prob.of Math Phys.

    • Related Report
      1995 Annual Research Report
  • [Publications] K.Mochizuki: "Blow-up and asymptotic behavior for quasilinear degenerate parabolic equations" GARC Proceedings,Seoul National University Edited Hi Jun Choe. to appear. (1995)

    • Related Report
      1994 Annual Research Report
  • [Publications] K.Mochizuki,K.Mukai: "Evistence and nonexistence of global solutions to fast diffusions with source" Methods and Applications of Analysis. 2(to appear). (1995)

    • Related Report
      1994 Annual Research Report
  • [Publications] K.Mochizuki,T,Motai: "On energy decay-nondecay problems for wave equations with nonlinear dissipative term in IRN" Journal of Mathematical Society of Japan. 47(to appear). (1995)

    • Related Report
      1994 Annual Research Report
  • [Publications] K.Kurata: "Continuity and Harnack's inequality for solutions of elliptic partial differential equations of second order" Indiana University Mathematical Journal. 43. 411-440 (1994)

    • Related Report
      1994 Annual Research Report
  • [Publications] K.Kurata: "On a backward estimate for solutions of parabolic differential equations and its applications to unique continuation" Advanced Studies in Pure Mathematics. 23. 247-257 (1994)

    • Related Report
      1994 Annual Research Report
  • [Publications] S.T.Kuroda,K.Kurata: "Product formulas and Error estimates" Proceedings of conference on Partial Differential Equations,Holzhase. to appear. (1994)

    • Related Report
      1994 Annual Research Report

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Published: 1994-04-01   Modified: 2016-04-21  

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