| Project/Area Number |
18K13445
|
|---|
| Research Category |
Grant-in-Aid for Early-Career Scientists
|
| Allocation Type | Multi-year Fund |
|---|
| Review Section |
Basic Section 12020:Mathematical analysis-related
|
|---|
| Research Institution | Tokyo University of Science |
|---|
Principal Investigator |
|
|---|
| Project Period (FY) |
2018-04-01 – 2022-03-31
|
| Project Status |
Completed (Fiscal Year 2021)
|
| Budget Amount *help |
¥3,380,000 (Direct Cost: ¥2,600,000、Indirect Cost: ¥780,000)
Fiscal Year 2021: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2020: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2019: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2018: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
|
|---|
| Keywords | 非有界な係数をもつ楕円型作用素 / 消散型波動方程式 / 漸近展開 / 高次漸近展開 / 半線形熱方程式系 / 特異極限 / 波動方程式 / Rellichの不等式 / 非線形消散型波動方程式 / 非線形波動方程式 / 外部問題 |
|---|
| Outline of Final Research Achievements |
In this research, we focus our attention to the development and applications to the theory of second order elliptic operators with unbounded coefficients. In the flamework of partial differential differential equations, we try to find essentials of linear problems and to apply it to the corresponding nonlinear problems.
One of the achievement in the linear problem is the Rellich inequalities in bounded domains. We found the necessary and sufficient conditions on the validity of Rellich inequalities with the Laplacian perturbed by the singular lower order terms.
For the nonlinear problem, we discussed the large time behavior of solutions to linear wave equations with space-dependent damping terms, blowup phenomena and global existence for the corresponding nonlinear problems.
|
| Academic Significance and Societal Importance of the Research Achievements |
非有界な係数をもつ2階楕円型作用素は様々な自然現象を記述する際に用いられる。この研究で、空間変数に依存する消散型波動方程式の長時間挙動に非有界な拡散構造を見ることができた。これは既存の研究からは得られない知見であり、同種の現象が他のモデルにも内在する可能性を示唆している。このことから、今後さらに非有界な係数という枠組みの重要性が高まったと考えている。
|
