Removability and asymptotic profile of dynamic singularities in parabolic partial differential equations
| Project/Area Number |
25610026
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| Research Category |
Grant-in-Aid for Challenging Exploratory Research
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| Allocation Type | Multi-year Fund |
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| Research Field |
Mathematical analysis
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| Research Institution | Tokyo Institute of Technology |
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Principal Investigator |
YANAGIDA Eiji 東京工業大学, 理工学研究科, 教授 (80174548)
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| Co-Investigator(Kenkyū-buntansha) |
KAN Toru 東京工業大学, 大学院理工学研究科, 助教 (60647270)
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| Project Period (FY) |
2013-04-01 – 2016-03-31
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| Project Status |
Completed (Fiscal Year 2015)
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| Budget Amount *help |
¥3,640,000 (Direct Cost: ¥2,800,000、Indirect Cost: ¥840,000)
Fiscal Year 2015: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2014: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2013: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
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| Keywords | 関数方程式 / 解析学 / 特異点 / 除去可能性 / 非線形 / 関数方程式の大域理論 / 特異性 / 安定性 / 漸近挙動 / 分岐構造 / 国際研究者交流 / 国際情報交換 / 多国籍 |
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| Outline of Final Research Achievements |
For the heat equation, we obtained a necessary and sufficient condition for the removability of singularities, and showed the existence of solutions whose singularities vary in time. Next, for Fujita-type equations, we studied properties of radially symmetric solutions and made clear the relation between initial values and convergence rates to the stationary solutions. For a semilinear parabolic equation with absorption, we made clear conditions for the removability of dynamic singularities, and showed that when non-removable, any singular solution can be classified into two types depending on the strength of singularities.
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Report
(4 results)
Research Products
(18 results)
