2001 Fiscal Year Final Research Report Summary
On the stracture of solutions of partial differential eauqtions
| Project/Area Number |
11640152
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (C)
|
| Allocation Type | Single-year Grants |
|---|
| Section | 一般 |
|---|
| Research Field |
Basic analysis
|
|---|
| Research Institution | Saitama University |
|---|
Principal Investigator |
SAKURAI Tsutomu Faculty of Science, SAITAMA UNIVERSITY, Associate Prpfessor, 理学部, 助教授 (40187084)
|
|---|
| Co-Investigator(Kenkyū-buntansha) |
FUKUI Toshizumi Faculty of Science, SAITAMA UNIVERSIY, Associate Professor, 理学部, 助教授 (90218892)
KOIKE Shigeaki Faculty of Science, SAITAMA UNIVERSIY, Associate Professor, 理学部, 助教授 (90205295)
YANO Tamaki Faculty of Science, SAITAMA UNIVERSIY, Profesor, 理学部, 教授 (10111410)
|
|---|
| Project Period (FY) |
1999 – 2000
|
| Keywords | Microlocal analysis / Dispersion wave / Asymptotic expantion / Viscosity solution / Optimal control / Real singularities / Comparison theorem |
|---|
| Research Abstract |
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.
|
