2002 Fiscal Year Final Research Report Summary
Asymptotic Profiles of Solutions to Nonlinear Convection-Diffusion Equations
| Project/Area Number |
13640177
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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., Graduate School of Education, Associate Professor, 大学院・教育学研究科, 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)
MATSUMOTO Toshitaka Hiroshima Univ., Graduate School of Science, Research Associate, 大学院・理学研究科, 助手 (20229561)
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| Project Period (FY) |
2001 – 2002
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| Keywords | Convection-diffusion equations / Global solutions in time / Blowup solutions / Asymptotic profiles of solutions / Stationary solutions |
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| Research Abstract |
The purpose of this research is to study the large time behavior of solutions and asymptotic profiles of decaying solutions to nonlinear convection-diffusion equations, and also to show the existence of global solutions. Especially, we focus on convection-diffusion diffusion equations related to chemotaxis and obtained the following results.
1. Every bounded solution of the Cauchy problem to a convection-diffusion equation in R^n (n 【greater than or equal】2) decays to zero as t 【tautomer】∞ and behaves like the heat kernel.
2. The existence of bounded solutions of the Cauchy problem mentioned just above is obtained under the smallness of L^1-norm of initial functions.
3. We consider a convection-diffusion equation without the chemical diffusion in a bounded interval under Neumann boundary conditions, and show the long time behaviour of solutions.
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