2011 Fiscal Year Final Research Report
Study on a chemotaxis equation in the two-dimensional whole space
| Project/Area Number |
21540182
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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 広島大学, 大学院・理学研究科, 教授 (40112172)
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| Research Collaborator |
YAMADA Tetsuya 広島大学, 大学院・理学研究科, 特任助教
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| Project Period (FY) |
2009 – 2011
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| Keywords | 非線形編微分方程式 / 走化性方程式 / Keller-Segel方程式 / 時間大域解 / 減衰評価 / 前進自己相似解 / 漸近挙動 |
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| Research Abstract |
We considered a simplified Keller-Segel equation(parabolic-elliptic system) in the two-dimensional whole space, which is a mathematical model of chemotaxis, and studied the global existence, uniqueness, boundedness and large-time behavior of nonnegative solutions to the Cauchy problem of the equation. We first established the local existence in time, uniqueness and regularity of mild solutions. In the subcritical case, we showed the global existence in time and decay estimates of nonnegative mild solutions without decay conditions of initial data, and then the convergence to a forward self-similar solution and convergence rates.
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