2010 Fiscal Year Final Research Report
Shape of the solutions and asymptotic analysis for the diffusive equations
| Project/Area Number |
19340036
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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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 | Tohoku University |
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Principal Investigator |
ISHIGE Kazuhiro 東北大学, 大学院・理学研究科, 教授 (90272020)
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| Co-Investigator(Kenkyū-buntansha) |
OGAWA Takayoshi 東北大学, 大学院・理学研究科, 教授 (20224107)
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) |
2007 – 2010
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| Keywords | 熱方程式 / 最大点挙動 / 等高面 / 大域的挙動 / 爆発問題 |
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| Research Abstract |
We study the shapes of the solutions of diffusive equations, and reveal the relationship between the movement of hot spots and the harmonic functions. Furthermore we studied the asymptotics of the solutions for the semilinear heat equations. In particular, we characterized the location of blow-up set for blow-up solutions, and also gave the decay estimates of the deference between global in time solutions and their asymptotics.
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