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Comprehensive Researches of Differential Equations

Research Project

Project/Area Number 03302008
Research Category

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

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

Principal Investigator

TANABE Hiroki  Osaka University, Faculty of Science, Professor, 理学部, 教授 (70028083)

Co-Investigator(Kenkyū-buntansha) KUSANO Takashi  Hiroshima University, Faculty of Science, Professor, 理学部, 教授 (70033868)
AIZAWA Sadakazu  Kobe University, Faculty of Science, Professor, 理学部, 教授 (20030760)
ICHINOSE Takashi  Kanazawa University, Faculty of Science, Professor, 理学部, 教授 (20024044)
KATO Junji  Tohoku University, Faculty of Science, Professor, 理学部, 教授 (80004290)
AGEMI Rentaro  Hokkaido University, Faculty of Science, Professor, 理学部, 教授 (10000845)
中尾 慎宏 (中尾 愼宏)  九州大学, 教養部, 教授 (10037278)
石井 仁司  中央大学, 理工学部, 教授 (70102887)
高野 恭一  神戸大学, 理学部, 教授 (10011678)
Project Period (FY) 1991 – 1992
Project Status Completed (Fiscal Year 1992)
Budget Amount *help
¥14,800,000 (Direct Cost: ¥14,800,000)
Fiscal Year 1992: ¥8,300,000 (Direct Cost: ¥8,300,000)
Fiscal Year 1991: ¥6,500,000 (Direct Cost: ¥6,500,000)
KeywordsOrdinary Differential Equations / Linear Equations / Hypergeometric Functions / Neutral Type / Functional Differential Equations / Partial Differential Equations / Mathematical Physics / Abstract Differential Equations / 接続問題 / 固有値問題 / 変分問題 / 数理物理 / 発展方程式
Research Abstract

As for ordinary differential equations in real domains solvability and properties of solutions were studied actively, and there were a number of remarkable results concerning the existence and non-existence of oscillatory or periodic solutions of Linear equations and of oscillatory and non-oscillatory solutions of neutral functional differential equations, etc. For equations containing an infinite delay it was discovered that equi-ultimate boundedness is not a consequence of ultimate boundedness unlike the case of a finite delay. Concerning ordinary differential equations in complex domains researches on hypergeometric functions of several independent variables were vigorous continuously, and significant results were established for the monodromy theory, homology theory, connection problems, etc. An extension of Painleve equations to partial differential equations was attempted with a satisfactory outcome. As for the control theory of retarded functional differential equations known re … More sults on controllability, observability, identifiability, etc. were greatly extended for evolution equations containing partial differential equations. As is noticed from what is stated above it should be remarked that the intercourse between ordinary differential equations and partial differential equations was greatly promoted. As for linear partial differential equations numerous results were obtained for initial value problems, boundary value problems, mixed problems, hypoellipticity, scattering problems, etc. The hypoellipticity of infinitely degenerate operators was deeply studied, and an example of an operator which is hypoelliptic but not microhypoelliptic was obtained. A Cauchy-Kovalevskaja type theorem for an equation with a vector valued time variable was established. Concerning nonlinear elliptic equations the existence and non-existence of global solutions or oscillatory solutions, asymptotic behavior at infinity, the method of viscosity solutions, etc. were continuously active. As for equations of mathematical physics or biology a great number of remarkable results were obtained for the decay of solutions of Navier-Stokes equations, equations of thermal convection and compressible viscous gases, variational problems containing a free boundary, the motion of an interface between two different kinds of substances, the Schrodinger limit of waves in plasma, scattering theory of wave or elasticity equations, the stability of traveling wave solutions, global solvabilty of quasi-linear abstract differential equations with applications to population dynamics, and so on. Less

Report

(3 results)
  • 1992 Annual Research Report   Final Research Report Summary
  • 1991 Annual Research Report
  • Research Products

    (27 results)

All Other

All Publications (27 results)

  • [Publications] 田辺 広城: "Fundamental solutions for linear retarded functional differential equations in Banach space" Funkcialaj Ekvacioj. 35. 149-178 (1992)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1992 Final Research Report Summary
  • [Publications] 松本 圭司,吉田 正章: "Certain reflection groups acting on symmetric domains of type IV" Memoirs of the Faculty of Science Kyushu,University Series A,Mathematics. 46. 115-128 (1992)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1992 Final Research Report Summary
  • [Publications] 原 惟行: "Non-existence of periodic solutions of the Lienard system" Journal of Mathematical Analysis and Applications. 159. 224-236 (1991)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1992 Final Research Report Summary
  • [Publications] 山中 健: "A Cauchy-Kovalevskaja type theorem in the Gevrey class with a vector-valued time variable" Communications in Partial Differential Equations. 17. 1457-1502 (1992)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1992 Final Research Report Summary
  • [Publications] 石井 仁司: "Perron's method for montone systems of second-order elliptic PDE's" Integral and Differential Equations. 5. 1-24 (1992)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1992 Final Research Report Summary
  • [Publications] 草野 栄,内藤 学: "Kiguradze classes for radial entire solutions of higher order quasi-linear elliptic equations" Hiroshima Journal of Mathematics. 22. 301-363 (1992)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1992 Final Research Report Summary
  • [Publications] 木村 俊房,高野 恭一: "関数論(新数学講座)" 朝倉書店, 171 (1991)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1992 Final Research Report Summary
  • [Publications] Hiroki TANABE: "Fundamental solutions for linear retarded functional differential equations in Banach space" Funkcialaj Ekvacioj. 35. 149-178 (1992)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1992 Final Research Report Summary
  • [Publications] Keiji MATSUMOTO & Masaaki YOSHIDA: "Certain reflection groups acting on symmetric domains of type IV" Memoirs of the Faculty of Science, Kyushu University Series A. 46. 115-128 (1992)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1992 Final Research Report Summary
  • [Publications] Tadayuki HARA: "Non-existence of periodic solutions of the Linear system" Journal of Mathematical Analysis and Applications. 159. 224-236 (1991)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1992 Final Research Report Summary
  • [Publications] Takeshi YAMANAKA: "A Cauchy-Kovalevskaja type theorem in the Gevrey class with a vector-valued time variable" Communications in Partial Differential Equations. 17. 1457-1502 (1992)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1992 Final Research Report Summary
  • [Publications] Hitoshi ISHII: "Perron's method for monotone systems of second-order elliptic PDE's" Integral and Differential Equations. 5. 1-24 (1992)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1992 Final Research Report Summary
  • [Publications] Takashi KUSANO & Manabu NAITO: "Kigradze classes for radial entire solutions of higher order quasi-linear elliptic equations" Hiroshima Journal of Mathematics. 22. 301-363 (1992)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1992 Final Research Report Summary
  • [Publications] Toshifusa KIMURA & Kyoichi TAKANO: Asakura Publishing Company. Theory of Functions of a complex variable (New Course of Mathematics), 171 (1991)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1992 Final Research Report Summary
  • [Publications] 田辺 広城: "Fundamental solutions for linear retarded functional differential equations in Banach space" Funkcialaj Ekvacioj. 35. 149-178 (1992)

    • Related Report
      1992 Annual Research Report
  • [Publications] 上見 練太郎: "The lifespan of classical solutions to nonlinear wave equations in two space dimensions" Hokkaido Mathematical Journal. 21. 517-542 (192)

    • Related Report
      1992 Annual Research Report
  • [Publications] 石井 仁司: "Viscosity solutions for a class of HamiltonーJacobi equations in Hilbert spaces" Journal of Functional Analysis. 105. 301-341 (1992)

    • Related Report
      1992 Annual Research Report
  • [Publications] 一瀬 孝: "On the Weyl quantized relativistic Hamiltonian,Operator Theory" Advances and Applications,Birkhauser. 57. 127-137 (1992)

    • Related Report
      1992 Annual Research Report
  • [Publications] 草野 尚: "Kiguradze classes for radial entire solutions of higher order quasiーlinear elliptic equations" Hiroshima Jounal of Mathematics. 22. 301-363 (1992)

    • Related Report
      1992 Annual Research Report
  • [Publications] 中尾 慎宏: "Existence of globaL smooth solutions to the initialーboundary value problem for the quasiーlinear wave equation with a degenerate dissipative term" Journal of Differential Equations. 98. 299-327 (1992)

    • Related Report
      1992 Annual Research Report
  • [Publications] Hiroki Tanabe: "Fundamental solutions for linear retarded functional differential equatins in Banach space" Funkcialaj Ekvacioj. 35. (1992)

    • Related Report
      1991 Annual Research Report
  • [Publications] Rentaro Agemi: "Blow up of solutions to nonlinear wave equations in two space dimensions" Manuscripta Mathematica. 73. 153-162 (1991)

    • Related Report
      1991 Annual Research Report
  • [Publications] Takashi Ichinose: "Remarks of the Weyl quantized relativistic Hamiltonian" Note di Matematica.

    • Related Report
      1991 Annual Research Report
  • [Publications] Hironobu Kimura.,Kyoichi Takano: "A reduction of Hamiltonian systems with multiーtime variables along a regular singularity" Proceedings of Japan Academy. 67. 226-231 (1991)

    • Related Report
      1991 Annual Research Report
  • [Publications] Jaroslav Jaros.,Takasi Kusano: "Oscillation properties of first order nonlinear functional differential equations of neutral type" Differential and Integral Equations. 4. 425-436 (1991)

    • Related Report
      1991 Annual Research Report
  • [Publications] Mitsuhiro Nakao: "Remarks on the existence and uniqueness of global decaying solutions of the nonlinear dissipative wave equations" Mathematische Zeitshcrift. 206. 265-276 (1991)

    • Related Report
      1991 Annual Research Report
  • [Publications] 木村 俊房,高野 恭一: "関数論(新数学講座)" 朝倉書店, 171 (1991)

    • Related Report
      1991 Annual Research Report

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

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