1993 Fiscal Year Annual Research Report

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 Institution	Keio 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)
Keywords	Free 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。

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

1993 Fiscal Year Annual Research Report

非線型及び大域解析学における諸問題の研究

Principal Investigator

谷 温之 慶應義塾大学, 理工学部, 助教授 (90118969)

Research Products

[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)

[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)

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

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

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

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

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

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

[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).

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

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

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

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

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

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

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

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

[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)

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

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

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

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

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

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

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

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

谷温之慶應義塾大学, 理工学部, 助教授 (90118969)