1993 年度実績報告書

非線型及び大域解析学における諸問題の研究

研究課題

研究課題/領域番号	05640220
研究機関	慶応義塾大学
研究代表者	谷温之慶應義塾大学, 理工学部, 助教授 (90118969)
研究分担者	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)
キーワード	Free boundary problem / Navier‐Stokes方程式 / Vortex motion / Morse flow / Quantization / Stabilization / WKB solution / Rauzy〓s conjecture
研究概要	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。

研究成果

(26件)

すべてその他

すべて文献書誌 (26件)

[文献書誌] 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)
[文献書誌] N.Tanaka: "Large‐time existence of compressible viscous and heat conductive surface waves" RFMS K〓ky〓roku,RIMS Kyoto Univ.824. 138-150 (1993)
[文献書誌] V.A.Solounikov: "Equilibrium figuers of slowly rotating viscous compressible ible baratropic expill0sy ligaid" Adv.Math.Sci.Appl.2. 139-145 (1993)
[文献書誌] N.Tanaka: "Large‐time existence of surface waves of compressible visceus fluid" Proc.Japan Acad. 69. 230-233 (1993)
[文献書誌] A.Tani: "The initcal value problem for the incompressible Narier‐Stokes equation with general slipboundary condition" Adv.Math.Sci.Appl.4(to appear).
[文献書誌] T.Nishiyama: "Solvability of the localiged induction equation for vortex motion" Cowm.Math Phys.(to appear).
[文献書誌] N.Kikuchi: "Holder estimates of solutions for difference‐differential equations of elliptic‐parabolic type" J.Geom.Anal.(to appear).
[文献書誌] N.Kikuchi: "A method of constructing Morse flows to variational functional" Nonlinear World. (to appear).
[文献書誌] 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).
[文献書誌] S.Koizumi: "Removable Banach function spaces on the theory interpolation extrapolation" Keio Sa.Eng.Reports. 46. (1993)
[文献書誌] I.Shiokawa: "Rings of normal and nonnormal numbers" Israel J.Math.84. 403-416 (1993)
[文献書誌] P.Arnoux: "Complexity of sequences defined by billiards in the cube" Bull.Soc.Math.Frace. (to appear).
[文献書誌] P.Arnoux: "Rauzy〓s conjecture on billiards in the cube" Tokyo J.Math.(to appear).
[文献書誌] H.Omori: "Non‐commutative complex projective space" Adv.Stu.Pure Math.22. 133-152 (1993)
[文献書誌] H.Omori: "The uniqueness of star products on Pn(C)." Proc.Symp in honour of Prof S.Buclin. 170-176 (1993)
[文献書誌] H.Omori: "A construction of a deformation quantization of a Poisson algebra" Proc.workshop on Geometry and its Appl.201-218 (1993)
[文献書誌] Y.Maeda: "The mean curvature of Jpuge orbits" Global Anal.in Modern Math.171-220 (1993)
[文献書誌] 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)
[文献書誌] H.Sano: "Stabilization of semilinear parabolic systems with boundary observations" 12th World Congress (IFAC). (to appear).
[文献書誌] H.Sano: "Inertial manifolds and stabilization of semilinear distribated parameter systems" 12th World Congress (IFAC). (to appear).
[文献書誌] H.Sano: "Stabilization of semilineas parabolic systems with boundary controls and observations an Approach via the inertial manifolds" European Control Conf.(to appear).
[文献書誌] M.Nakano: "On the WKB solutions of 3rd order linear ordinary differential equations" Proc.4th Int.Conf.on dif‐eq.(to appear).
[文献書誌] S.Shimomura: "Asymptotic expansions and Stokes multipliers of the confluent by hypergeometric function PHI,I" Proc.Royal Soc.Edinburgh. 123. 1165-1177 (1993)
[文献書誌] Y.Yamaura: "A free boundary problem for minimal surface equation" Boll.Uni.Mat.Itab.(to appear).
[文献書誌] Y.Yamaura: "A uniform estimate of the perimeter for minimizes of a free boundary problem" Rend.Mat.Appl.(to appear).
[文献書誌] Y.Yamaura: "The regularity of minimizers of radially symmetric free boundary problem" Am.Univ.Ferrara. (to appear).

1993 年度 実績報告書

非線型及び大域解析学における諸問題の研究

研究代表者

谷 温之 慶應義塾大学, 理工学部, 助教授 (90118969)

研究成果

[文献書誌] 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)

[文献書誌] N.Tanaka: "Large‐time existence of compressible viscous and heat conductive surface waves" RFMS K〓ky〓roku,RIMS Kyoto Univ.824. 138-150 (1993)

[文献書誌] V.A.Solounikov: "Equilibrium figuers of slowly rotating viscous compressible ible baratropic expill0sy ligaid" Adv.Math.Sci.Appl.2. 139-145 (1993)

[文献書誌] N.Tanaka: "Large‐time existence of surface waves of compressible visceus fluid" Proc.Japan Acad. 69. 230-233 (1993)

[文献書誌] A.Tani: "The initcal value problem for the incompressible Narier‐Stokes equation with general slipboundary condition" Adv.Math.Sci.Appl.4(to appear).

[文献書誌] T.Nishiyama: "Solvability of the localiged induction equation for vortex motion" Cowm.Math Phys.(to appear).

[文献書誌] N.Kikuchi: "Holder estimates of solutions for difference‐differential equations of elliptic‐parabolic type" J.Geom.Anal.(to appear).

[文献書誌] N.Kikuchi: "A method of constructing Morse flows to variational functional" Nonlinear World. (to appear).

[文献書誌] 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).

[文献書誌] S.Koizumi: "Removable Banach function spaces on the theory interpolation extrapolation" Keio Sa.Eng.Reports. 46. (1993)

[文献書誌] I.Shiokawa: "Rings of normal and nonnormal numbers" Israel J.Math.84. 403-416 (1993)

[文献書誌] P.Arnoux: "Complexity of sequences defined by billiards in the cube" Bull.Soc.Math.Frace. (to appear).

[文献書誌] P.Arnoux: "Rauzy〓s conjecture on billiards in the cube" Tokyo J.Math.(to appear).

[文献書誌] H.Omori: "Non‐commutative complex projective space" Adv.Stu.Pure Math.22. 133-152 (1993)

[文献書誌] H.Omori: "The uniqueness of star products on Pn(C)." Proc.Symp in honour of Prof S.Buclin. 170-176 (1993)

[文献書誌] H.Omori: "A construction of a deformation quantization of a Poisson algebra" Proc.workshop on Geometry and its Appl.201-218 (1993)

[文献書誌] Y.Maeda: "The mean curvature of Jpuge orbits" Global Anal.in Modern Math.171-220 (1993)

[文献書誌] 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)

[文献書誌] H.Sano: "Stabilization of semilinear parabolic systems with boundary observations" 12th World Congress (IFAC). (to appear).

[文献書誌] H.Sano: "Inertial manifolds and stabilization of semilinear distribated parameter systems" 12th World Congress (IFAC). (to appear).

[文献書誌] H.Sano: "Stabilization of semilineas parabolic systems with boundary controls and observations an Approach via the inertial manifolds" European Control Conf.(to appear).

[文献書誌] M.Nakano: "On the WKB solutions of 3rd order linear ordinary differential equations" Proc.4th Int.Conf.on dif‐eq.(to appear).

[文献書誌] S.Shimomura: "Asymptotic expansions and Stokes multipliers of the confluent by hypergeometric function PHI,I" Proc.Royal Soc.Edinburgh. 123. 1165-1177 (1993)

[文献書誌] Y.Yamaura: "A free boundary problem for minimal surface equation" Boll.Uni.Mat.Itab.(to appear).

[文献書誌] Y.Yamaura: "A uniform estimate of the perimeter for minimizes of a free boundary problem" Rend.Mat.Appl.(to appear).

[文献書誌] Y.Yamaura: "The regularity of minimizers of radially symmetric free boundary problem" Am.Univ.Ferrara. (to appear).

1993 年度実績報告書

谷温之慶應義塾大学, 理工学部, 助教授 (90118969)