| Project/Area Number |
22540200
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Basic analysis
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| Research Institution | Kyushu Institute of Technology |
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Principal Investigator |
SENBA Takasi 九州工業大学, 工学(系)研究科(研究院), 教授 (30196985)
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| Co-Investigator(Kenkyū-buntansha) |
鈴木 智成 九州工業大学, 工学(系)研究科(研究院), 教授 (00303173)
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| Project Period (FY) |
2010-04-01 – 2015-03-31
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| Project Status |
Completed (Fiscal Year 2014)
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| Budget Amount *help |
¥3,510,000 (Direct Cost: ¥2,700,000、Indirect Cost: ¥810,000)
Fiscal Year 2013: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2012: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2011: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2010: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
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| Keywords | 走化性方程式 / 後方自己相似解 / 定常解 / 安定性 / 非線形拡散 / アトラクター / 関数方程式論 / 爆発解 / 振動解 / 偏微分方程式論 / 走化性方程式系 / 爆発 |
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| Outline of Final Research Achievements |
From 2010 to 2014, we consider properties of solutions to chemotaxis system. In particular, we consider stability of backward self-similar solutions and stationary solutions.
First, we consider properties of backward self-similar solutions. The backward self-similar solutions are one of typical blowup solutions. We showed some stability of the solutions. The solutions are not so many. However, it became clear by our research that many solutions have similar properties to the backward self-similar solutions.
Next, we consider stability of stationary solutions to chemotaxis system. It was well known that radial stationary solutions are stable in two dimensional case. We showed that radial stationary solutions are stable also in high dimensional cases. Moreover, by using stability, we construct oscillatory solutions and infinite time blowup solutions.
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