On new approch for wellposedness for degenerate and singular Keller-Segel systems
| Project/Area Number |
24540186
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Basic analysis
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| Research Institution | Kyushu University |
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Principal Investigator |
SUGIYAMA Yoshie 九州大学, 大学院・数理学研究院, 教授 (60308210)
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| Project Period (FY) |
2012-04-01 – 2015-03-31
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| Project Status |
Completed (Fiscal Year 2014)
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| Budget Amount *help |
¥5,200,000 (Direct Cost: ¥4,000,000、Indirect Cost: ¥1,200,000)
Fiscal Year 2014: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2013: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2012: ¥2,080,000 (Direct Cost: ¥1,600,000、Indirect Cost: ¥480,000)
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| Keywords | 退化放物型方程式 / Keller-Segel系 / 初期値問題の局所適切性 / 解の一意性 / 解の有限時間爆発 / Navier-Stokes方程式 / Keller-Segel方程式系 / 時間局所解の適切性 / 有限時間爆発解 / 解の正値性と保存則 / 時間大域解 / 非線形拡散 / 特異放物型 / 退化放物型 / 定常解 / 有限伝播性 |
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| Outline of Final Research Achievements |
The Keller-Segel system contains several parameters which cause numerous structures such as linear, degenerate and singular type of PDE. In particular, the degenerate type contains the unknown function as the coefficients breaking down uniform ellipticity, which makes the problem more difficult in comparison with the other types.
The Keller-Segel system itself is characterized as the parabolic-parabolic and parabolic-elliptic both of provide us an important research theme. Indeed, we need to handle these types in accordance with the characteristic features of equations. In this talk, we shall bring a focus onto the parabolic-parabolic and parabolic-elliptic Keller-Segel systems of the singular and degenerate types and show uniqueness of weak solutions in the class of Hoelder continuous functions.
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Report
(4 results)
Research Products
(34 results)
