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非線型及び大域解析学における諸問題の研究

Research Project

Project/Area Number 05640220
Research Category

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

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

Principal Investigator

谷 温之  慶應義塾大学, 理工学部, 助教授 (90118969)

Co-Investigator(Kenkyū-buntansha) 下村 俊  慶應義塾大学, 理工学部, 講師 (00154328)
前田 吉昭  慶應義塾大学, 理工学部, 助教授 (40101076)
国松 昇  慶應義塾大学, 理工学部, 助教授 (70051662)
塩川 宇賢  慶應義塾大学, 理工学部, 教授 (00015835)
菊池 紀夫  慶應義塾大学, 理工学部, 教授 (80090041)
Project Period (FY) 1993
Project Status Completed (Fiscal Year 1993)
Budget Amount *help
¥2,000,000 (Direct Cost: ¥2,000,000)
Fiscal Year 1993: ¥2,000,000 (Direct Cost: ¥2,000,000)
KeywordsFree boundary problem / Navier‐Stokes方程式 / Vortex motion / Morse flow / Quantization / Stabilization / WKB solution / Rauzy〓s conjecture
Research Abstract

非線型解析学及び大域解析学に於ける諸問題を、従来の枠組にとらわれないで総合的に研究することを目的にして1年間研究を続けてきました。この間次のような結果が得られました。
1.(1)圧縮性Navier‐Stokes方程式の自由境界問題の時間大域解が、表面張力が作用している際には、バロトロピック流体星と一般の表面波動の時、静止状態の近くで1意に存在する。更に、バロトロピック流体星に対してはやはり静止状態の近くではあるが、ゆっくりと回転する平衡状態が存在する。
(2)非圧縮性Euler方程式から得られる渦方程式のうちで、最も簡単であるが有名な渦糸方程式はSchr〓dinger方程式に変換して調べられているが、実はそれら同じものではない可能性がある事が指摘された。
2.楕円‐放物型差分微分方程式の解のH〓lder評価、半線放物型方程式系の安定化問題に対する結果。
3.Poisson algebraの変形量子化の構成、Gauge軌道の平均曲率についての結果。
4.3階線形常微分方程式のWKB解の構成、合流型超幾何関数の漸近展開とStokes multiplierについての結果。
5.正規数からなる環の構成、3次元ビリヤードの生成する符号列のcomplexityに関するRauzy予想の肯定的解決。
これらを証明する際に用いられた方法・考察は他の多くの問題にも適用でき、将来新しい事実が判明するものと期待される。

Report

(1 results)
  • 1993 Annual Research Report
  • Research Products

    (26 results)

All Other

All Publications (26 results)

  • [Publications] V.A.Solonnikoo: "Evolution free boundary problem for equations of motion of viscous compressible barotropie liquid liquid." Lecture Notes in Math.1530. 30-55 (1993)

    • Related Report
      1993 Annual Research Report
  • [Publications] N.Tanaka: "Large‐time existence of compressible viscous and heat conductive surface waves" RFMS K〓ky〓roku,RIMS Kyoto Univ.824. 138-150 (1993)

    • Related Report
      1993 Annual Research Report
  • [Publications] V.A.Solounikov: "Equilibrium figuers of slowly rotating viscous compressible ible baratropic expill0sy ligaid" Adv.Math.Sci.Appl.2. 139-145 (1993)

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      1993 Annual Research Report
  • [Publications] N.Tanaka: "Large‐time existence of surface waves of compressible visceus fluid" Proc.Japan Acad. 69. 230-233 (1993)

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      1993 Annual Research Report
  • [Publications] A.Tani: "The initcal value problem for the incompressible Narier‐Stokes equation with general slipboundary condition" Adv.Math.Sci.Appl.4(to appear).

    • Related Report
      1993 Annual Research Report
  • [Publications] T.Nishiyama: "Solvability of the localiged induction equation for vortex motion" Cowm.Math Phys.(to appear).

    • Related Report
      1993 Annual Research Report
  • [Publications] N.Kikuchi: "Holder estimates of solutions for difference‐differential equations of elliptic‐parabolic type" J.Geom.Anal.(to appear).

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      1993 Annual Research Report
  • [Publications] N.Kikuchi: "A method of constructing Morse flows to variational functional" Nonlinear World. (to appear).

    • Related Report
      1993 Annual Research Report
  • [Publications] N.Kikuchi: "On the higher integrability of the gradients of the solutions a difference partial differential systems of elliptic‐parabolic type" Math.Zeit. (to appear).

    • Related Report
      1993 Annual Research Report
  • [Publications] S.Koizumi: "Removable Banach function spaces on the theory interpolation extrapolation" Keio Sa.Eng.Reports. 46. (1993)

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      1993 Annual Research Report
  • [Publications] I.Shiokawa: "Rings of normal and nonnormal numbers" Israel J.Math.84. 403-416 (1993)

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      1993 Annual Research Report
  • [Publications] P.Arnoux: "Complexity of sequences defined by billiards in the cube" Bull.Soc.Math.Frace. (to appear).

    • Related Report
      1993 Annual Research Report
  • [Publications] P.Arnoux: "Rauzy〓s conjecture on billiards in the cube" Tokyo J.Math.(to appear).

    • Related Report
      1993 Annual Research Report
  • [Publications] H.Omori: "Non‐commutative complex projective space" Adv.Stu.Pure Math.22. 133-152 (1993)

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      1993 Annual Research Report
  • [Publications] H.Omori: "The uniqueness of star products on Pn(C)." Proc.Symp in honour of Prof S.Buclin. 170-176 (1993)

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      1993 Annual Research Report
  • [Publications] H.Omori: "A construction of a deformation quantization of a Poisson algebra" Proc.workshop on Geometry and its Appl.201-218 (1993)

    • Related Report
      1993 Annual Research Report
  • [Publications] Y.Maeda: "The mean curvature of Jpuge orbits" Global Anal.in Modern Math.171-220 (1993)

    • Related Report
      1993 Annual Research Report
  • [Publications] H.Sano: "Modified Gro〓wall〓s inequality and its application to stabrilization problem for semilinear parabolic systems" Systems and Control Letters. 21(to appear). (1993)

    • Related Report
      1993 Annual Research Report
  • [Publications] H.Sano: "Stabilization of semilinear parabolic systems with boundary observations" 12th World Congress (IFAC). (to appear).

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      1993 Annual Research Report
  • [Publications] H.Sano: "Inertial manifolds and stabilization of semilinear distribated parameter systems" 12th World Congress (IFAC). (to appear).

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      1993 Annual Research Report
  • [Publications] H.Sano: "Stabilization of semilineas parabolic systems with boundary controls and observations an Approach via the inertial manifolds" European Control Conf.(to appear).

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      1993 Annual Research Report
  • [Publications] M.Nakano: "On the WKB solutions of 3rd order linear ordinary differential equations" Proc.4th Int.Conf.on dif‐eq.(to appear).

    • Related Report
      1993 Annual Research Report
  • [Publications] S.Shimomura: "Asymptotic expansions and Stokes multipliers of the confluent by hypergeometric function PHI,I" Proc.Royal Soc.Edinburgh. 123. 1165-1177 (1993)

    • Related Report
      1993 Annual Research Report
  • [Publications] Y.Yamaura: "A free boundary problem for minimal surface equation" Boll.Uni.Mat.Itab.(to appear).

    • Related Report
      1993 Annual Research Report
  • [Publications] Y.Yamaura: "A uniform estimate of the perimeter for minimizes of a free boundary problem" Rend.Mat.Appl.(to appear).

    • Related Report
      1993 Annual Research Report
  • [Publications] Y.Yamaura: "The regularity of minimizers of radially symmetric free boundary problem" Am.Univ.Ferrara. (to appear).

    • Related Report
      1993 Annual Research Report

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Published: 1993-04-01   Modified: 2016-04-21  

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