Analysis of dynamic singularities in nonlinear evolution equations
| Project/Area Number |
22654020
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| Research Category |
Grant-in-Aid for Challenging Exploratory Research
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| Allocation Type | Single-year Grants |
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| Research Field |
Global 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, 大学院・理工学研究科, 教授 (80174548)
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| Project Period (FY) |
2010 – 2012
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| Project Status |
Completed (Fiscal Year 2012)
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| Budget Amount *help |
¥3,170,000 (Direct Cost: ¥2,600,000、Indirect Cost: ¥570,000)
Fiscal Year 2012: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2011: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2010: ¥700,000 (Direct Cost: ¥700,000)
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| Keywords | 関数方程式の大域理論 / 非線形 / 拡散 / 放物型 / 特異性 / 偏微分方程式 / 定性理論 / 反応拡散系 / ダイナミクス |
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| Research Abstract |
In this project, we studied the qualitative properties of solutions with moving singularities for various nonlinear parabolic partial differential equations. First, we investigated conditions for the global existence of solutions with singularities. Next, under certain conditions, the solution converges to a singular steady state. Furthermore, we showed that the convergence rate depends on the decay rate of initial values. This implies that there are two types of singular steady states that arecharacterized by the convergence rate.
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Report
(4 results)
Research Products
(22 results)
