Research on Evolution Equations Describing Anomalous Diffusion

2015 Fiscal Year Final Research Report

• Project/Area Number: 25400163
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Mathematical analysis
• Research Institution: Kobe University
• Principal Investigator: Akagi Goro 神戸大学, システム情報学研究科, 准教授 (60360202)
• Co-Investigator(Renkei-kenkyūsha): Shirakawa Ken 千葉大学, 教育学部, 准教授 (50349809) ; Ueda Yoshihiro 神戸大学, 大学院海事科学研究科, 准教授 (50534856) ; Ishiwata Tetsuya 芝浦工業大学, システム理工学部, 教授 (50334917) ; Takeuchi Shingo 芝浦工業大学, システム理工学部, 准教授 (00333021)
• Project Period (FY): 2013-04-01 – 2016-03-31
• Keywords: 非線形解析 / 発展方程式 / 異常拡散 / 非線形拡散 / 変分法

Outline of Final Research Achievements

In natural and social phenomena, diffusion phenomena often play a crucial role. The classical theory on diffusion phenomena has already been established in the last century; however, there arose many diffusion phenomena presenting peculiar appearance beyond the scope of the classical theory. Such exceptional diffusion phenomena are classified as "anomalous diffusion" and attracting much interest in various fields. In this research project, a mathematical theory is developed in order to analyze anomalous diffusion. More precisely, the so-called "nonlinear diffusion" models, which are formulated in terms of nonlinear partial differential equations, are mainly treated. Furthermore, fundamental issues such as the well-posedness of each equation are justified and asymptotic behaviors and profiles of solutions are revealed. By virtue of solving each problem, we have developed a mathematical theory for anomalous diffusion.

Free Research Field

解析学