Study on the blowup solution and time global solution for the nonlinear drift-diffusion equation system
| Project/Area Number |
24540201
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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 |
Global analysis
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| Research Institution | Muroran Institute of Technology |
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Principal Investigator |
KUROKIBA MASAKI 室蘭工業大学, 工学(系)研究科(研究院), 教授 (60291837)
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| Project Period (FY) |
2012-04-01 – 2016-03-31
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| Project Status |
Completed (Fiscal Year 2015)
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| Budget Amount *help |
¥5,200,000 (Direct Cost: ¥4,000,000、Indirect Cost: ¥1,200,000)
Fiscal Year 2015: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2014: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2013: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2012: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
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| Keywords | 非線形移流拡散方程式系 / 有限時間爆発解 / 多成分系 / エントロピー / シャノンの不等式 / 初期値問題 / 空間高次元 / 2次モーメント / 高次元 / 移流拡散方程式系 / 時間大域解 / 走化性 / 閾値 / 移流拡散方程式 / 爆発解 / 粘菌 / 空間2次元 |
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| Outline of Final Research Achievements |
We have considered a drift-diffusion system which is not one component.At first, we have studied a drift-diffusion system on bounded domain in two space dimension. Then we have performed the blowup analysis such as the formation of collapses and collapsemass separations. And we have discussed the blow-up conditions for multicomponent drift-diffusion model in two space dimension and higher dimensions, respectively. Moreover We have shown that the local solvability of the solution in the weighted L2 spaces and the extention of the functional space for the solution in two space dimension.In higher dimension case, we have applied the Shannon entropy inequality to lead the blow up condition for a drift-diffusion system.
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Report
(5 results)
Research Products
(22 results)
