| Project/Area Number |
12640206
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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 | Nagoya University |
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Principal Investigator |
ISHIGE Kazuhiro Nagoya, University,Gradnate School of Manthematics, Asociated, Proffes., 大学院・多元数理科学研究科, 助教授 (90272020)
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| Co-Investigator(Kenkyū-buntansha) |
OSADA Hirofumi Nagoya, University,Gradnate School of Manthematics, Asociated, Proffes., 大学院・多元数理科学研究科, 教授 (20177207)
MIYAKE Masatake Nagoya, University,Gradnate School of Manthematics, Asociated, Proffes., 大学院・多元数理科学研究科, 教授 (70019496)
NAWA Hayato Nagoya, University,Gradnate School of Manthematics, Asociated, Proffes., 大学院・多元数理科学研究科, 助教授 (90218066)
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| Project Period (FY) |
2000 – 2001
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| Project Status |
Completed (Fiscal Year 2001)
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| Budget Amount *help |
¥2,900,000 (Direct Cost: ¥2,900,000)
Fiscal Year 2001: ¥1,300,000 (Direct Cost: ¥1,300,000)
Fiscal Year 2000: ¥1,600,000 (Direct Cost: ¥1,600,000)
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| Keywords | heat ezuation. / blow-up prololem / neumann condition / nonneqstibe solution / コーシー問題 |
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| Research Abstract |
We study the uniqueness of nonnegative solutions of the diffusive equations in unbounded domains. We first study the problem with Minoru Murata, and obtain an optimal sufficient condition for the uniqueness of the nonnegative solutions of the whole Euclidean space to hold. Furthermore Ishige study the uniqueness of nonnegative solutions of the Cauchy-Dirichlet problem to the diffusive equations in unbounded domains, and obtain an optimal sufficient condition for the uniiqueness tohold.
Next we study the blow-up problem for a semilinear parabolic equation with larqe diffusion. We prove that the solution blows up only near some points determined by the projection of the initial data to the second Neumann eigenspace. In order to study this problem, we need to study the long-time behavior of the nonnegative solution of the heat equation, that is, the Neumann eigenfunctions.
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