2018 Fiscal Year Final Research Report
On the asymptotics and well-posedness for Keller-Segel system of degenerate and singular type
| Project/Area Number |
15K04961
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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 |
Mathematical analysis
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| Research Institution | Osaka University (2018)
Kyushu University (2015-2017) |
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Principal Investigator |
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| Project Period (FY) |
2015-04-01 – 2019-03-31
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| Keywords | 退化放物型方程式 / Keller-Segel系 / 漸近解析 / 非自明定常解 |
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| Outline of Final Research Achievements |
We investigated asymptotic analysis at infinite time with the degenerate Keller-Segel system. More precisely, we proved the existence of nontrivial stationary solutions of the Keller-Segel system, and further proved the fact that the profiles for the Keller-Segel system, which are time-evolving solutions, have the same stationary solution at time infinity. The research results have been published in IUMJ in 2018 as a joint research with Mr. Jose Carrillo.
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| Free Research Field |
非線形偏微分方程式論
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| Academic Significance and Societal Importance of the Research Achievements |
退化楕円型方程式の変分問題を解くことに帰着し，Keller-Segel系の非自明な定常解の存在証明を確立している．同問題の解析には，退化性が誘引する正則性欠如を克服する必要がある．我々は，球対称性を担保することで解のサポートコンパクト性を保証し，解析を容易にする手法を確立している．同手法は多様な退化型方程式系の解析に有効である．
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