| Project/Area Number |
15540199
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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 | Tokyo Gakugei University |
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Principal Investigator |
MIZOGUCHI Noriko Tokyo Gakugei University, Education, Assistant professor, 教育学部, 助教授 (00251570)
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| Co-Investigator(Kenkyū-buntansha) |
YANAGIDA Eiji Tohoku University, Mathematics, Professor, 大学院・理学研究科, 教授 (80174548)
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| Project Period (FY) |
2003 – 2004
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| Project Status |
Completed (Fiscal Year 2004)
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| Budget Amount *help |
¥3,600,000 (Direct Cost: ¥3,600,000)
Fiscal Year 2004: ¥1,600,000 (Direct Cost: ¥1,600,000)
Fiscal Year 2003: ¥2,000,000 (Direct Cost: ¥2,000,000)
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| Keywords | semilinear heat equation / blowup / incomplete blowup / continuation of solution / backward self-similar solution / 半線形放物型方程式 / 爆発集合 / Neumann境界条件 / supercritical / 逆向き自己相似 |
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| Research Abstract |
In this research, we investigated a blowup problem for a semilinear diffusion equation with power nonlinerity. The blowup rate for the equation under the Neumann boundary condition or the Dirichlet boundary condition in a non-convex domain is considered. A well-lnown result due to Giga Kohn cannot be applied to these cases, so we showed the blowup is of type I making use of Liouville type theorem. Here a solution of the equation is said to exhibit the type I blowup if the blowup rate is as same as that of solutions to the corresponding ordinary equation. Next, the 1 location of the blowup set of solutions to the Cauchy-Neumann problem is described by the property of the domain in the case of large diffusion. We also studied the continuation after blowup for supercritical exponent in the Sobolev sense. Solutions blowing up in finite time and being a classical solution for all time after blowup with various behaviors as time tends to infinity. Moreover, we got a solution which blows up in finite time and becomes regular immediately after the blowup time and blows up again.
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