2004 Fiscal Year Final Research Report Summary
On the analysis of blowup phenomena for a nonlinear parabolic equation
| 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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| Keywords | semilinear heat equation / blowup / incomplete blowup / continuation of solution / backward self-similar solution |
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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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Research Products
(28 results)
