2000 Fiscal Year Final Research Report Summary
Analysis on Singularities of Solutions to Nonlinear Partial Differential Equations
| Project/Area Number |
11640173
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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 |
Basic analysis
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| Research Institution | Hiroshima University |
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Principal Investigator |
NAGAI Toshitaka Hiroshima Univ., Graduate School of Science, Professor, 大学院・理学研究科, 教授 (40112172)
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| Co-Investigator(Kenkyū-buntansha) |
KURA Takeshi Hiroshima Univ., Graduate School of Science, Research Associate, 大学院・理学研究科, 助手 (10161720)
IKEHATA Ryo Hiroshima Univ., Faculty of Education, Associate Professor, 教育学部, 助教授 (10249758)
YOSHIDA Kiyoshi Hiroshima Univ., Faculty of Integrated Arts and Sciences, Professor, 総合科学部, 教授 (80033893)
KOBAYASHI Takayuki Kyushu Inst.of Technology, Faculty of Engineering, Associate Professor, 工学部, 助教授 (50272133)
SENBA Takasi Miyazaki Univ., Faculty of Technology, Associate Professor, 工学部, 助教授 (30196985)
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| Project Period (FY) |
1999 – 2000
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| Keywords | Nonlinear partial differential equations / Advection-diffusion equations / Global solutions in time / Blowup solutions / Self-similar solutions / Stationary solutions |
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| Research Abstract |
The purpose of this research is to study the behavior of solutions to nonlinear partial differential equations by analyzing singularities of finite-time blowup solutions. Especially, we focus on two types of advection-diffusion equations (parabolic-elliptic system, parabolic system) and obtained the following results.
1. The possibility of finite-time blowup of nonradial solutions to the parabolic-elliptic system.
2. Finite-time blowup solutions to the parabolic system have δ-function singularities at isolated blow-up points in two-dimensional domains
3. The structure of self-similar solutions to the parabolic system.
4. The structure of steady states to the parabolic system.
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