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On the stracture of solutions of partial differential eauqtions

偏微分方程解的结构

基本信息

批准号：
11640152
负责人：
SAKURAI Tsutomu
金额：
$ 2.24万
依托单位：
Saitama University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
1999
资助国家：
日本
起止时间：
1999 至 2000
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-11640152/
关键词：
Microlocal analysis Dispersion wave Asymptotic expantion Viscosity solution Optimal control Real singularities Comparison theorem 解析的準楕円性 Symplectic characteristic 擬微分作用素特異点 Bellman方程式

项目摘要

The head investigator considered the asymptotic behavior of the surface waves of viscous incomplessible fluids. The suaface waves are governed by the Euler equation with the free boundary condition on the surface. We studied the dispersive behavior of the solutions to the linearlized equation. By using the Airy integral, we gave the asymptotic formula for the solutions at degenerate points. We also studied the coherent states of the light in the quantum mecanics. The coherent states are not mutually orthogonal but make a complete system of the quantum states of the light. Making use of the coherent states expantion, we obtained another derivation for the fundamental solutions to the Harmonic oscilators.The head investigator writing a book on the partial differential equations. Some of the above results will be included in this book.

首席研究员考虑了粘性不完全流体表面波的渐近行为。表面波由表面自由边界条件下的欧拉方程控制。我们研究了线性化方程解的色散性。利用Airy积分，给出了退化点处解的渐近公式.我们还研究了量子力学中光的相干态。相干态不是相互正交的，而是构成光的量子态的完整系统。利用相干态展开，我们得到了谐振子基本解的另一种推导方法。上述部分结果将包含在本书中。