2010 Fiscal Year Final Research Report
New development of the qualitative theory of nonlinear parabolic and elliptic equations
| Project/Area Number |
19204014
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| Research Category |
Grant-in-Aid for Scientific Research (A)
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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 | Tokyo Institute of Technology (2010)
Tohoku University (2007-2009) |
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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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| Co-Investigator(Kenkyū-buntansha) |
IZUMI Takagi 東北大学, 大学院・理学研究科, 教授 (40154744)
NAITO Yuki 愛媛大学, 大学院・理工学研究科, 教授 (10231458)
OGAWA Takayoshi 東北大学, 大学院・理学研究科, 教授 (20224107)
EI Shin-ichiro 九州大学, 大学院・数理学研究院, 教授 (30201362)
ISHIGE Kazuhiro 早稲田大学, 理工学術院, 教授 (90272020)
TANAKA Kazunaga 早稲田大学, 理工学術院, 教授 (20188288)
NINONMIYA Hiro 龍谷大学, 理工学部, 准教授 (90251610)
TONEGAWA Yoshihiro 北海道大学, 大学院・理学研究科, 教授 (80296748)
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| Project Period (FY) |
2007 – 2010
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| Keywords | 関数方程式の大域理論 |
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| Research Abstract |
We carried out the investigation about the structure of solutions of nonlinear parabolic and elliptic equations. Our main results are as follows : Next, we studied the existence and uniqueness of solutions with moving singularities for a nonlinear parabolic partial differential equation. We also showed that there exists a solution with a moving singularity that changes its type suddenly., and made clear the asymptotic behavior of singular solutions that converges to a singular steady state. We also studied a chemotaxis system, and made clear the structure of self-similar solutions that blows up by concentrating to a point in finite time.
For a reaction-diffusion system, which is called a Gierer-Meinhardt system, we studied the mathematical structure of pattern formation, and also made clear the behavior of time-dependent solutions.
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