Correlation research for non-local interaction system and the mass transport conservation law

2014 Fiscal Year Final Research Report

• Project/Area Number: 23654059
• Research Category: Grant-in-Aid for Challenging Exploratory Research
• Allocation Type: Multi-year Fund
• Research Field: Global analysis
• Research Institution: Tohoku University
• Principal Investigator: OGAWA Takayoshi 東北大学, 理学(系)研究科(研究院), 教授 (20224107)
• Co-Investigator(Kenkyū-buntansha): NAGAI Toshitaka 広島大学, 大学院理学研究科, 名誉教授 (40112172) ; KUROKIBA Masaki 室蘭工業大学, 大学院工学研究科, 准教授 (60291837)
• Project Period (FY): 2011-04-28 – 2015-03-31
• Keywords: 移流拡散方程式 / 質量輸送問題 / 非局所的相互作用 / 非線形偏微分方程式論 / 時間大域解 / 有限時刻爆発 / 不等式の最良定数 / 閾値

Outline of Final Research Achievements

Models described by drift-diffusion equations having a typical mass transport structure, it is understood and classified as one of the non-local interaction system. In this research, we consider the global behavior of the solution to a semi-linear drift-diffusion system in two and three-dimensional cases. In addition, we also study a system of degenerate drift-diffusion equations and make it clear the global behavior
of the weak solution. Furthermore, we find the global structure of the solutions are quite similar to the one of the nonlinear disspersive equations and between the critical exponents, we classified the global behavior of the solution and find the threshold value of the global existence.

Free Research Field

実解析学・応用解析学