Modern Analysis for the Equations of Mathematical Science

数学科学方程的现代分析

• 批准号: 04402001
• 负责人: NISHIDA Takaaki
• 金额: $ 9.66万
• 依托单位: KYOTO UNIVERSITY
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for General Scientific Research (A)
• 财政年份: 1992
• 资助国家: 日本
• 起止时间: 1992 至 1994
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-04402001/
• 关键词: Hyperbolic P.D.E.; Stochastic Diff.Eq.; Fluid dynamical equations; Solvable lattice models; Dynamical System; Bifurcation problems; Structure of solution space; Computer assisted proof; 量子力学の方程式; 分岐問題; 計算機支援証明; ホモクリニック倍分岐; Schrodinger方程式; 散乱理

Main theme is the investigation of the structure of the solution and the structure of the solution space for the system of the differential equations in the mathematical science.(1) Investigation for the characterization of the wellposedness of the hyperbolic partial differential equation, specially the effective hyperbolicity for the equation which has triple chracteristic roots. Propagation of singularities along the bicharacteristics(2) Investigations of the solutions of stochastic differential equations, especially the expansion of the Donsker's delta function by the wiener chaos using the Levi-sum method which constructs the heat kernel from the Gauss kernel. Approximation scheme for the heat kernel using the Donsker's delta function(3) Investigation for the structure of the space of states for solvable lattice models. Explicit formula for the correlation function for the six-vertex model using the representation of quantum groups(4) Investigation of bifurcations and chaos in the Dynamical systems. Appearance of the geometric strange attractors by small perturbation of the degenerate vector field which has triple zero characteristic values. Codimension two bifurcations of homoclinic or heteroclinic orbits, specially infinitely many numbers of homoclinic doubling bif.(5) Bifurcation problems for the equations of fluid dynamics. Investigations and proof of the stationary and Hopf bifurcations for the free surface problems using the computer assisted proof

主要主题是研究溶液结构和数学科学中微分方程系统的解决方案空间的结构。（1）研究表征双曲线部分微分方程的良好性，特别是方程的有效双曲线，具有三重铬基动力。使用LEVI-SUM方法沿Wiener Chaos扩展了随机微分方程溶液的奇异性（2）研究，尤其是Donsker Delta功能的扩展，该方法使用LEVI-SUM方法构建了从高斯kernel中构造热核的方法。使用Donsker的Delta功能（3）调查的热内核的近似方案，用于可解决的晶格模型的状态空间结构。使用量子组（4）研究动力学系统中分叉和混乱的量子组的表示，用于六个vertex模型的相关函数的显式公式。几何奇怪吸引子的外观通过归化矢量场的小扰动，具有三重零特征值。编码的两个同型或杂斜轨道的分叉，特别是无限量的同型侧联合BIF。（5）流体动力学方程的分叉问题。使用计算机辅助证明的自由表面问题的固定和HOPF分叉的调查和证明

项目成果

Htay Aung Win,Takaaki Teramoto: "Navier-Stokes Flow an inclined Plane:Downward Periodic motion" J. Mathematics Kyoto University. (1993)

Htay Aung Win，Takaaki Teramoto：“纳维-斯托克斯流倾斜平面：向下周期运动”J. 京都大学数学。

Takashi Okaji: "Equations of evolution on the Heisenberg group II" J.Math.Kyoto Univ.33. 973-988 (1993)

Takashi Okaji：“海森堡第二群的演化方程”J.Math.Kyoto Univ.33。

Takaaki Nomura: "Manifold of primitive idempotents in a Jordan-Hilbert algebra" J.Math.Soc.Japan. 45. 37-58 (1993)

Takaaki Nomura：“Jordan-Hilbert 代数中的原始幂等流形”J.Math.Soc.Japan。

T.Nishida,Y.Teramoto and H.Yoshihara: "Eigenvalue problems of the parameter dependent system of ord.diff.eg.and computer aided proof" Kokyuroku RIMS Kyoto Univ.865. 57-64 (1994)

T.Nishida、Y.Teramoto 和 H.Yoshihara：“ord.diff.eg. 参数相关系统的特征值问题和计算机辅助证明”Kokyuroku RIMS 京都大学 865。

M.Jimbo, T.Miwa, Y.Ohta: "Structure of the space of states in RSOS models" Int.J.Mod.Phys.A,8. 1457-1477 (1993)

M.Jimbo、T.Miwa、Y.Ohta：“RSOS 模型中状态空间的结构”Int.J.Mod.Phys.A，8。