| Budget Amount *help |
¥4,680,000 (Direct Cost: ¥3,600,000、Indirect Cost: ¥1,080,000)
Fiscal Year 2019: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2018: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2017: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2016: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2015: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
|
|---|
| Outline of Final Research Achievements |
I studied nonlinear partial differential equations in the complex domain, and investigated in detail the behavior of singularities of solutions. The structure of singularities is completely clarified in the following two cases: the case of first order Briot-Bouquet type partial differential equations, and the case of first order nonlinear totally characteristic partial differential equations. In the case of higher order partial differential equations and q-difference partial differtential equations, many new findings have been obtained.
|
| Academic Significance and Societal Importance of the Research Achievements |
複素領域での常微分方程式の特異点の研究は, ２０世紀初頭に一応の完成を見た。その後は, 数学や物理などの多くの分野で基本言語の一つとして活用されている。偏微分方程式の特異点の研究においても, 基礎的部分が十分に整理されれば, 多くの数学や物理などの分野において重要な役割を果たすと期待される。
|
