Solutions of Differential Equations and Applications

微分方程的解及其应用

• 批准号: 06302012
• 负责人: MOCHIZUKI Kiyoshi
• 金额: $ 7.17万
• 依托单位: Tokyo Metropolitan University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Co-operative Research (A)
• 财政年份: 1994
• 资助国家: 日本
• 起止时间: 1994 至 1995
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-06302012/
• 关键词: differential equations; applied mathematics; numerical analysis; plasma physics; fluid mechanics; quantum mechanics; 量子論; 非線形発展方程式; 経路積分; 波動方程式; 逆問題; 符号理論; 数理物理; 作用素論; 非線形拡散方程式

The study of differential equations extends in various directions. Among them we, the investigators of this project, have mainly concerned with the problems related Physics, Engineering and other applied sciences. To develop mathematical researches in these fields, we need joint studies with many related investigators. We made plan and managed several symposiums under the following three principles ;1. To proceed cooperations with investigotors of Applied mathematics, Applied Physics, Numerical Analysis and Information Science.2. To recomend young mathematician, especially graduate students, to participate in the symposium and to give lectires.3. To cell to foreign investigators who are visiting Japan to participate in the symposium.We actually or ganized morethan 20 symposiums in these two years. In each of them we could invite investigators of the related fields cited above. Moreover, among 300 lectures anounced in these symposiums, morethan 30 lectures are given by graduate students and also 30 lectures are given by foreign investigators.These plan brought us fruitfull results, and this project is executed successfully. Details are sumonarized in the 「Report of Research Results」 of this project.

微分方程的研究向各个方向延伸。其中我们作为该项目的研究者主要关注物理、工程学和其他应用科学相关的问题。要开展这些领域的数学研究，我们需要与许多相关研究者进行联合研究。我们根据以下三个原则策划并组织了多次研讨会； 1．与应用数学、应用物理、数值分析、信息科学领域的研究者开展合作。 2．推荐青年数学家，特别是研究生参加会议并讲学。 3．敬请来日参加研讨会的外国研究者参加。这两年我们实际上组织了20多次研讨会。在每个项目中，我们都可以邀请上述相关领域的研究人员。另外，在这些研讨会上公布的300个讲座中，有30多个是研究生的讲座，还有30多个外国研究者的讲座。这些计划给我们带来了丰硕的成果，这个项目执行得很成功。详细内容汇总于本项目的「研究成果报告」中。

项目成果

J.Kato: "Stability property and phase space" Rockey Mountain J.Math. 25. 315-338 (1995)

J.Kato：“稳定性性质和相空间”Rockey Mountain J.Math。

K.Kurata: "Continuity and Harnack's inequality for solutions of elliptic partial differential equations of second order" Indiana University Mathematical Journal. 43. 411-440 (1994)

K.Kurata：“二阶椭圆偏微分方程解的连续性和 Harnack 不等式”印第安纳大学数学杂志。

K. Mochizuki, R.Suzuki: "Critical exponent and critical blow-up for quasilinear parabolic equations" Isreal Journal Mathematics. (In press).

K. Mochizuki、R.Suzuki：“拟线性抛物线方程的临界指数和临界爆炸”Isreal Journal Mathematics。

K. Kajitani, A. Baba: "The Cauchy problem for Schrodinger type equations" Bull. Sci. Math.119. 459-473 (1995)

K. Kajitani、A. Baba：“薛定谔型方程的柯西问题”Bull。

Kiyoshi Mochizuki and Ryuichi Suzuki: "Critical exponent and critical klow-up for quauilinear parabolic equations" Israel Joarnal Mathematies. (To appear).

Kiyoshi Mochizuki 和 Ryuichi Suzuki：“拟线性抛物型方程的临界指数和临界 klow-up” Israel Joarnal Mathematics。