Synthetic study on differential equations

微分方程的综合研究

• 批准号: 07304013
• 负责人: AGEMI Rentaro
• 金额: $ 9.92万
• 依托单位: HOKKAIDO UNIVERSITY
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (A)
• 财政年份: 1995
• 资助国家: 日本
• 起止时间: 1995 至 1996
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-07304013/
• 关键词: ordinary differential equations; partial differential equations; elliptic differential equations; parabolic differential equations; hyperbolic differential equations; Fourier integral operators; existence of global solutions; blow-up of solutions /

Head of this project held the meetings at Tokyo, July 1995 and at Sapporo, July 1996 and decided the schedules of conferences organized by investigators. In the conferences on differential equations held at Tokyo, December 1995 and 1996, there were approximately two hundred researchers from the whole country. The investigators also opened the fifteen local conferences, for example, The 20^<th> and 21^<st> Sapporo symposium on partial differential equations (Hokkaido Univ.), The analytic partial differential equations and related topics in ordinary differential equations (Nagoya Univ.), Symposium on nonlinear partial differential equations (Tokyo Metropolitan Univ.), etc. In the above conferences we obtained many significant research results in the following fields (see the report on this project in detail),(1) The qualitive theory of ordinary differential equations,(2) The local theory of partial differential equations(3) The integral operators and elliptic equations(4) The geometric theory of parabolic equations(5) The global theory of evolution equations(6) The nonlinear equations in theoritical physics

该项目的负责人于1995年7月在东京举行了会议，并于1996年7月在萨波罗举行了会议，并决定了调查人员组织的会议时间表。在1995年12月和1996年在东京举行的微分方程会议上，全国大约有200名研究人员。研究人员还开设了15个当地会议，例如，在偏微分方程（北海道大学）上的20^<th>和21^<t> sapporo研讨会，普通微分方程的分析部分微分方程和相关主题（Nagoya Univ。会议我们在以下领域中获得了许多重要的研究结果（请参阅该项目的报告），（1）普通微分方程的重要理论，（2）局部微分方程的局部理论（3）积分操作者和椭圆形方程（4）抛物性等式的几何理论（5）非全球方程式（6）非元素方程（6）非细小方程（6）

项目成果

Rentaro, Agemi: "The null condition and global existence of solutions to systems of wave equations with different speeds" Series on Advance in Mathematics for Applied Sciences. (in press). (1997)

Rentaro，Agemi：“不同速度波动方程组解的零条件和全局存在性”应用科学数学进展系列。

Hitoshi, Ishii: "Degenerate pavobolic. PDEs with discontinuities and general evolutions of surface" Advance Differential equations. 1. 51-72 (1996)

Hitoshi, Ishii：“简并帕沃波型。具有不连续性的偏微分方程和表面的一般演化”高级微分方程。

Takashi, Ichinose: "Estemate of the difference between the Kac operator and Schrodiger semigroup" Comm. Marh. Phys.(in press).

Takashi, Ichinose：“Kac 算子和 Schrodiger 半群之间差异的估计”Comm。

Kyoichi, Takano: "A normal form of Hamiltonian systems of several time variables with a regular singurality" J. Diff. Eqs.127. 337-364 (1966)

Kyoichi, Takano：“具有规则奇异性的多个时间变量的哈密顿系统的范式”J. Diff。

Mitsuhiro Nakao: "Decay of solutions of the wave equation with a local nonlinear dissipation" Math.Ann.305. 403-417 (1996)

Mitsuhiro Nakao：“具有局部非线性耗散的波动方程解的衰减”Math.Ann.305。