2010 Fiscal Year Final Research Report
Self-similarity and singularity of solutions for nonlinear parabolic PDEs
| Project/Area Number |
20540210
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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 |
Global analysis
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| Research Institution | Ehime University (2009-2011)
Kobe University (2008) |
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Principal Investigator |
NAITO Yuki 愛媛大学, 大学院・理工学研究科, 教授 (10231458)
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| Co-Investigator(Kenkyū-buntansha) |
ISHII Katsuyuki 神戸大学, 海事科学研究科, 准教授 (40232227)
KUWAMURA Masataka 神戸大学, 人間発達環境学研究科, 准教授 (30270333)
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| Co-Investigator(Renkei-kenkyūsha) |
SUZUKI Takashi 大阪大学, 基礎工学研究科, 教授 (40114516)
SENBA Takashi 九州工業大学, 工学研究科, 教授 (30196985)
ISHIGE Kazuhiro 東北大学, 理学研究科, 教授 (90272020)
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| Project Period (FY) |
2008 – 2010
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| Keywords | 非線形偏微分方程式 / 自己相似性 / 解の爆発 / 特異性 / 定常問題 |
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| Research Abstract |
The structure of self-similar solutions for semilinear heat equations is studied, and the role of self-similar solutions in the problem of asymptotic behavior of time-glabal solutions is investigated. In particular, new results on the structure of self-similar solutions for semilinear heat equations with Sobolev critical nonlinarity are obtained. Furthermore, the applications to the nonlinear problem involving chemotaxis system are studied.
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