Investigations on Linear and Nonlinear Mathematical Analysis with Applications

线性和非线性数学分析及其应用研究

• 批准号: 60540088
• 负责人: YANAGIHARA Niro
• 金额: $ 1.02万
• 依托单位: Chiba University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for General Scientific Research (C)
• 财政年份: 1985
• 资助国家: 日本
• 起止时间: 1985 至 1986
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-60540088/
• 关键词: Nonlinear difference equations; Nonlinear partial differential equations; Infinite dimensional linear dynamical systems; Banach bundle; 準線形波動方程式; 高炉内の熔鉄; 2次元プラズマ; 劣調和函数; フラグメン・リンデレーフ型条件; システム理論; バナッハ・バンドル

[1] Study on nonlinear difference equationsAnalytic solutions, their existency and asymptotic representations, are investigated for nonlinear difference equations of the first order or higher order. We wish to determine the structure of solution manifolds for these equations.[2] Study on nonlinear partial differential equations3-dimensional stationary Stokes equations are investigated when the boundary conditions of the first kind and of the second kind are given simultaneously. Free boundary problem in a shaft furnace is investigated with penalty method, and further treated numerically. 2-dimensional equilibrium plasma with symmetric cross section is investigated, both theoretically and numerically. Nonlinear evolution equations of Moser's type are investigated with the general Newton method. Cauchy problems for quasi-linear wave equations are investigated. Existency of global solutions will be further investigated.[3] Study on system theoryLinear dynamical systems with infinite dimensional state spaces are investigated. The necessary and sufficient conditions for the existence of fine moduli spaces are obtained.

[1]研究非线性差异分析溶液，其存在和渐近表示，研究了一阶或更高阶的非线性差异方程。我们希望确定这些方程的解决方案歧管的结构。[2]当同时给出第一类和第二种边界条件时，研究了非线性偏微分方程3维固定的Stokes方程。用惩罚方法研究了轴炉中的自由边界问题，并进一步进行数值处理。在理论上和数值上研究了具有对称横截面的二维平衡等离子体。通过一般的牛顿方法研究了Moser's类型的非线性演化方程。研究了准线性波方程的库奇问题。将进一步研究全球解决方案的存在。[3]研究了具有无限尺寸空间的系统理论线性动力学系统。获得了精细模量空间的必要条件。

项目成果

Niro Yanagihara: Journal of the Mathematical Society of Japan. 37. 569-603 (1985)

Niro Yanagihara：日本数学会杂志。

Hideo Kawarada;Hideyuki Koshigoe: Technical Reports of Mathematical Sciences,Chiba University. No.20. (1986)

Hideo Kawarada；Hideyuki Koshigoe：数学科学技术报告，千叶大学。

Shin Kawase;Niro Yanagihara: SIAM Journal on Control and Optimization. (1987)

Shin Kawase；Niro Yanagihara：SIAM​​ 控制与优化杂志。

Hidenobu Yoshida: "On subharmonic functions dominated by certain functions" Israel Journal of Mathematics. 54. 366-380 (1986)

吉田秀信：“论受某些函数支配的次谐波函数”以色列数学杂志。

Niro Yanagihara: Archive for Rational Mechanics and Analysis. 91. 169-192 (1986)

Niro Yanagihara：理性力学和分析档案。