On the asymptotics and well-posedness for Keller-Segel system of degenerate and singular type
| Project/Area Number |
15K04961
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (C)
|
| Allocation Type | Multi-year Fund |
|---|
| Section | 一般 |
|---|
| Research Field |
Mathematical analysis
|
|---|
| Research Institution | Osaka University (2018)
Kyushu University (2015-2017) |
|---|
Principal Investigator |
|
|---|
| Project Period (FY) |
2015-04-01 – 2019-03-31
|
| Project Status |
Completed (Fiscal Year 2018)
|
| Budget Amount *help |
¥4,680,000 (Direct Cost: ¥3,600,000、Indirect Cost: ¥1,080,000)
Fiscal Year 2017: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2016: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2015: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
|
|---|
| Keywords | 退化放物型方程式 / Keller-Segel系 / 漸近解析 / 非自明定常解 / 退化型 / 閾値 / 定常解 / 有限伝播性 / Navier-Stokes方程式 / 退化放物型 / 特異放物型 / 初期値問題の時間局所適切性 / 爆発解 / Keller-Segel 系 / chemotaxis / well-posedness / Navier-Stokes 方程式 / Uniqueness |
|---|
| 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.
|
| 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．
|
Report
(5 results)
Research Products
(30 results)
