| Project/Area Number |
26887027
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| Research Category |
Grant-in-Aid for Research Activity Start-up
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| Allocation Type | Single-year Grants |
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| Research Field |
Mathematical analysis
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| Research Institution | Kyushu University |
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Principal Investigator |
SEKI YUKIHIRO 九州大学, 数理(科)学研究科(研究院), 助教 (50728970)
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| Project Period (FY) |
2014-08-29 – 2016-03-31
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| Project Status |
Completed (Fiscal Year 2015)
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| Budget Amount *help |
¥2,080,000 (Direct Cost: ¥1,600,000、Indirect Cost: ¥480,000)
Fiscal Year 2015: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2014: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
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| Keywords | 特異性解析 / Type II / 半線形熱方程式 / 調和写像流方程式 / type II 爆発 / 非線形放物型方程式 |
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| Outline of Final Research Achievements |
In this research I studied singularity formation of solutions of nonlinear heat equations with power-like nonlinearity as a typical model equation of second-order nonlinear PDEs. The phenomenon of loosing boundedness of solution in a finite time is called blow-up of solution. Classification of blow-up solutions are one of the main theme of this topic since 1980s. This problem has deep relation with the nonlinear structure of the equation. In this research I constructed, by means of matched asymptotic expansions, blow-up solutions that exhibit non-self-similar blow-up mechanisms in the case that the power is equal to a threshold value, which haven't been dealt with in the literature. As its application, I studied singularity formation of harmonic map heat flow with values in a sphere and obtained particular solutions that exhibit non-self-similar singularity, which was unknown in high space dimensions.
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