Study on the blowup solution and time global solution for the nonlinear drift-diffusion equation system

2015 Fiscal Year Final Research Report

• Project/Area Number: 24540201
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Global analysis
• Research Institution: Muroran Institute of Technology
• Principal Investigator: KUROKIBA MASAKI 室蘭工業大学, 工学(系)研究科(研究院), 教授 (60291837)
• Project Period (FY): 2012-04-01 – 2016-03-31
• 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

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.

Free Research Field

解析学