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Study of various problems in mathematical physics

Research Project

Project/Area Number 07404003
Research Category

Grant-in-Aid for Scientific Research (A)

Allocation TypeSingle-year Grants
Section一般
Research Field 解析学
Research InstitutionOchanomizu University (1997-1998)
The University of Tokyo (1995-1996)

Principal Investigator

KANEKO Akira  Ochanomizu University, Faculty of Sciences, Professor, 理学部, 教授 (30011654)

Co-Investigator(Kenkyū-buntansha) KASAHARA Yuji  Ochanomizu University, Faculty of Sciences, Professor, 理学部, 教授 (60108975)
TAKEO Fukiko  Ochanomizu University, Faculty of Sciences, Professor, 理学部, 教授 (40109228)
KIKUCHI Fumio  Univ.of Tokyo, Graduate School of Math.Sci., Professor, 大学院・数理科学研究科, 教授 (40013734)
YAMADA Michio  Univ.of Tokyo, Graduate School of Math.Sci., Professor, 大学院・数理科学研究科, 教授 (90166736)
MIMURA Masayasu  Univ.of Tokyo, Graduate School of Math.Sci., Professor, 大学院・数理科学研究科, 教授 (50068128)
成田 希世子  お茶の水女子大学, 理学部, 助手 (80189208)
塚田 和美  お茶の水女子大学, 理学部, 教授 (30163760)
真島 秀行  お茶の水女子大学, 理学部, 教授 (50111456)
松崎 克彦  お茶の水女子大学, 理学部, 助教授 (80222298)
山本 昌宏  東京大学, 大学院・数理科学研究科, 助教授 (50182647)
北田 均  東京大学, 大学院・数理科学研究科, 助教授 (40114459)
バランディン アレクサン  東京大学, 大学院・数理科学研究科, 教授 (00280959)
薩摩 順吉  東京大学, 大学院・数理科学研究科, 教授 (70093242)
Project Period (FY) 1995 – 1998
Project Status Completed (Fiscal Year 1998)
Budget Amount *help
¥37,700,000 (Direct Cost: ¥37,700,000)
Fiscal Year 1998: ¥8,500,000 (Direct Cost: ¥8,500,000)
Fiscal Year 1997: ¥6,800,000 (Direct Cost: ¥6,800,000)
Fiscal Year 1996: ¥6,700,000 (Direct Cost: ¥6,700,000)
Fiscal Year 1995: ¥15,700,000 (Direct Cost: ¥15,700,000)
Keywordsmathematical physics / partial differential equations / tomography / hyperfunctions / inverse problems / トモゲラフィ / 複素モーメント問題 / パターン形成 / 非線型非平衡系 / 有限要素法 / セレンディピティ要素 / 双曲型逆問題 / カルレマン評価 / ウェーブレット / 乱流
Research Abstract

On continuation of Gevrey class solutions of linear partial differential equations, we found new results describing the possibility of continuation in terms of the multiplicity of the characteristic and Gevrey index.
On the asymptotic behavior of solutions, we found a generalization of Liouville's theorem to the existence of infra-exponential global solutions. In problem of pattern formation of some bacteria, we presented a mathematical model and via computer simulation we recovered the known 2D patterns and found that they come from phase transition.
On the uniquensee of the inverse problems for hyperbolic equations, we presented a best Lip-schitz stability under weaker conditions on the coefficients. In the reconstruction problem of plane figures, we presented efficient reconstruction algorithm and showed its stability in unique case. In non-unique case, we introduced various weight functions and found interesting patterns as reconstruction images maximizing them.
For the Reissner-Mindlin plate model we exploited new stable mixed rectangular finite element and showed that on the thin limit it goes to the Kirchhoff model without causing locking. On the shell model in turbulence, we examined chaos solution obeying the same similarity law and obtained its Lyapunov spectra. Finding that they contain components of significant magnitude only at some typical wave numbers, we singled out an asymptotic expression for the large attrac-tor dimension, and verified its good concordance with numerical calculation. We constructed bi-orthogonal wavelets adapted to integral operators invariant under scale transformation, and gave its applications.

Report

(5 results)
  • 1998 Annual Research Report   Final Research Report Summary
  • 1997 Annual Research Report
  • 1996 Annual Research Report
  • 1995 Annual Research Report
  • Research Products

    (42 results)

All Other

All Publications (42 results)

  • [Publications] 菊地文雄: "Interpolation error estimates of a rnodified 8-node serendipity finite element." UTMS. 96-51. 1-19 (1996)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] 山田道夫・佐々木: "Biological wavelet adapted to integral operators and thoir applications" Japan J.Indust.Appl.Math.14. 257-297 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] 金子 晃: "On the global solvalility of linear partial differential equations with corntant coefficients in the space of real analytic functions" Banach Center Publications. 33. 149-160 (1996)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] 金子 晃: "On continuation of gevren class solutions of linear partial differential eguations" J.Math.Sci.Univ.of Tokyo. 4. 551-593 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] 金子 晃: "Liouville type theorem for solutions of infra-exponen-tial growth of linear partial differential equations with constant coefficients" Natural Sci.Report Ochanomizu Univ.49. 1-5 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Balanclin・金子晃: "Maximum entropy Method for sign-altering functions" Inverse Problems. 15. 445-463 (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] 金子 晃: "超函数入門(新版)" 東京大学出版会, 442 (1996)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] 金子 晃: "偏微分方程式入門" 東京大学出版会, 346 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] KIKUCHI,Fumio: "Interpolation error estimates of a modified 8-node serendipity finite element" UTMS. 96-51. 1-19 (1996)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] YAMADA,Michio and F.Sasaki: "Biological wavelet adapted to integral operators and their applications" JJIAM. 14. 257-297 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] KANEKO,Akira: "On the global solvability of linear partial differential equations with constant coefficients in the space of real analytic functions" Banach Center Publications. 33. 149-160 (1996)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] KANEKO,Akira: "On continuation of Gevrey class solutions of linear partial differential equations" J.Math.Sci.Univ.of Tokyo. 4. 551-593 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] BALANDIN,A.and A.Kaneko: "Maximum Entropy Method for sign-altering functions" Inverse Problems. 15. 445-463 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] KANEKO,Akira: "Liouville type theorem for solutions of infra-exponential growth of linear partial differential equations with constant coefficients" Natural Sci.Report Ochanomizu Univ.49. 1-5 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] KANEKO,Akira: Introduction to Hyperfunctions (New Edition) (In Japanese). Univ.of Tokyo Press, 442 (1996)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] KANEKO,Akira: Introduction to Partial Differential Equations. Univ.of Tokyo Press, 346 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] 金子 晃: "Liour'lle type theorem for solutions of in fra-exponetial growth of lenear partial differential eqations with constant cofficeontc" Natural Sci.Report Ochanomizu Univ. 49. 1-5 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] 金子 晃・Huang Lei: "Recnstruction of plane figures from two projections" Discrete Tomography(Ed.Herman,Kuba). 1(to appear). (1999)

    • Related Report
      1998 Annual Research Report
  • [Publications] Balandin,金子 晃: "Maxinum Entropy Method for sign-altering functions" Incerse Problems. 15. 445-463 (1999)

    • Related Report
      1998 Annual Research Report
  • [Publications] 金子 晃: "On extension of analytic solutions of lirear partial differential equations" Amer.Math.Soc.Transl. 188. 105-110 (1999)

    • Related Report
      1998 Annual Research Report
  • [Publications] 塚田和美・清田由紀: "Curvature tensors and Sinser in variant of four-dimensional homugeneons spaces" Comment Math.Univ.Carloinae. (近刊).

    • Related Report
      1998 Annual Research Report
  • [Publications] 塚田和美: "The modnli space of locally homogeneous spaces and locally homogeneous spaces which are not locally isometric to globally spaces" Proceedings DGA98. (近刊).

    • Related Report
      1998 Annual Research Report
  • [Publications] 金子 晃: "On continuation of Gevrey class solutions of linear partial differential equations" Journal of Math Su′ univ of Tokyo. 4. 551-593 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] 金子 晃: "幾何学的トモグラフィ" 津田塾大数学計算機科学研究所報. 13. 54-66 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] 金子 晃: "On continuation of Gevrey class solutions of linear partial differential equations" Proc.7th Intem Gllog on Diff Eg(VSP). 197-204 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] 塚田 和美: "Holomorphic maps of compact generaliged Hopf manifolds" Geometricae Dedicata. 68. 61-71 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] 松崎 克彦: "Structural Stalility of Kleinian groups" Michigam Math. J.44. 21-36 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] 古谷 希世子: "Mixed Problem for wave eanations with obl:gue boundary condition" GAKUTO Intern.Ser.Math.Sui.&Appl.10. 69-74 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] 金子 晃: "偏微分方程式入門" 東京大学出版会, 346 (1998)

    • Related Report
      1997 Annual Research Report
  • [Publications] 金子 晃: "On continuation of gevrey class solutions of linear partial diffenantial eqations" J.Math.Sci.Unis.of Tokyo. (刊行予定).

    • Related Report
      1996 Annual Research Report
  • [Publications] 金子 晃: "On the global soluability of linear partial differntial equations with constant coefficients in the space of real Cirrerlytic functions." Banach Center Publications. 33. 149-160 (1996)

    • Related Report
      1996 Annual Research Report
  • [Publications] 菊地 文雄: "辺要素タイプの有限要素法の特色と実用化" 機械の研究. 49-1. 111-117 (1997)

    • Related Report
      1996 Annual Research Report
  • [Publications] 菊地 文雄: "Interpolation error estimates of a modified 8-node serendipity finite element" UTMSプレプリントシリーズ. 96-51. 1-19 (1997)

    • Related Report
      1996 Annual Research Report
  • [Publications] 山本 昌宏: "Stability of Lipschitz type in determination of initial haet distribution" J.Ineq Appl.1-1. 73-83 (1997)

    • Related Report
      1996 Annual Research Report
  • [Publications] 山本 昌宏: "On uniqueness in multidimensional hyperbolic inverse problems less regular case" UTMSプレプリントシリーズ. 97-1. 1-24 (1997)

    • Related Report
      1996 Annual Research Report
  • [Publications] 金子 晃: "超函数入門[新版]" 東京大学出版会, 442 (1996)

    • Related Report
      1996 Annual Research Report
  • [Publications] 金子晃: "Some problens on continnation of regnlar solutions of partial differential eguations" UTMS 95-43. 1-15 (1995)

    • Related Report
      1995 Annual Research Report
  • [Publications] 菊地文雄(石井): "An inproved 4-node gnadrilateral plate bending element of the Reissner Mindlin type" UTMS 95-3. 1-19 (1995)

    • Related Report
      1995 Annual Research Report
  • [Publications] 菊地文雄(福原誠): "An iteration method for fimte element analysis of magneto static problems" Lecture Notes in Num.Anal. 14. 93-105 (1995)

    • Related Report
      1995 Annual Research Report
  • [Publications] 山田道夫(大木谷): "Energy and entrogy fluxes in shell models of turbulence" Proc.Intern.Conf.Dyn.Sys.and Chaos. 197-200 (1995)

    • Related Report
      1995 Annual Research Report
  • [Publications] 山田道夫(大木谷): "Phenomenological theory of Lyapunov spectrum of a shell model of turbulence" Phys.Rev.Letter. (1996)

    • Related Report
      1995 Annual Research Report
  • [Publications] 山田道夫(佐々木): "Biorthogonal wavelet adapted to in tegral operators and their applications" JJIAN. (1996)

    • Related Report
      1995 Annual Research Report

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Published: 1995-04-01   Modified: 2022-09-26  

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