| Project/Area Number |
15K21058
|
|---|
| Research Category |
Grant-in-Aid for Young Scientists (B)
|
| Allocation Type | Multi-year Fund |
|---|
| Research Field |
Geometry
Basic analysis
|
|---|
| Research Institution | Kyushu Institute of Technology |
|---|
Principal Investigator |
Noda Takahiro 九州工業大学, 大学院工学研究院, 准教授 (10596555)
|
|---|
| Project Period (FY) |
2015-04-01 – 2020-03-31
|
| Project Status |
Completed (Fiscal Year 2019)
|
| Budget Amount *help |
¥4,030,000 (Direct Cost: ¥3,100,000、Indirect Cost: ¥930,000)
Fiscal Year 2018: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2017: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2016: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2015: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
|
|---|
| Keywords | 微分式系の理論 / 偏微分方程式の幾何学 / 微分式系 / 微分式系の幾何学 / 接触変換群 / 三階の偏微分方程式系 / 幾何学 / 微分方程式 |
|---|
| Outline of Final Research Achievements |
Differential equation is an important mathematical concept for analyzing various phenomena in the world. In particular, second-order partial differential equations provide typical examples describing various important model phenomena in mathematical physics and engineering, including the wave equation (hyperbolic type), heat equation (parabolic type), and Laplace equation (elliptic type). As mentioned above, second order equations have been traditionally studied.
On the other hand, for third-order partial differential equations, several progress has been made, including the discovery of special equations (integrable systems) such as the KdV equation. However, it still seemed insufficient from the point of view of the geometric foundation. Hence, in this research project, I formulated rigorously a geometric theory of third-order partial differential equations.including a classification into several classes and characterization of several aspects.
|
| Academic Significance and Societal Importance of the Research Achievements |
微分方程式は, 世の中の様々な現象を分析するための重要な数学的概念である。ニュートンの運動方程式をはじめとして、他にも波動方程式(双曲型)、熱方程式(放物型)、ラプラス方程式(楕円型)など、数理物理学や工学における種々の重要なモデル現象を記述できる。この微分方程式は本来解析学の分野に属する研究対象であるが、これを幾何学の分野の研究対象(微分式系)として視覚化し、空間図形的観点から微分方程式がもつ様々な性質を浮きぼりにするのが私の研究内容である。
|
