Theory for the analysis on the motion of localized patterns in higher dimesional spaces

2016 Fiscal Year Final Research Report

• Project/Area Number: 24340019
• Research Category: Grant-in-Aid for Scientific Research (B)
• Allocation Type: Partial Multi-year Fund
• Section: 一般
• Research Field: General mathematics (including Probability theory/Statistical mathematics)
• Research Institution: Hokkaido University (2014-2016); Kyushu University (2012-2013)
• Principal Investigator: EI Shin-Ichiro 北海道大学, 理学(系)研究科(研究院), 教授 (30201362)
• Project Period (FY): 2012-04-01 – 2017-03-31
• Keywords: 反応拡散系 / 局在解 / 相互作用

Outline of Final Research Achievements

In this project, we aimed to develop mathematical technique to analyze the interacting motion of localized patterns and succeeded to get results for the motions for a curved surface, asymmetric localized patterns and traveling localized ones. Clearly speaking, we first clarified the relation between geometrical properties of a surface and motions of interacting patterns. We also derived the equation explicitly to determine a stable spatial distribution of patterns. Secondly, we established a general theory to deal with asymmetric patterns and applied it to the analysis of interacting motion of two camphor discs on water surface. We also checked the theoretical prediction in a real experiment. Finally, we mention to succeed to construct stable pairs of traveling patterns by using the interaction between fast and slow traveling ones. The result is shown to be applicable to the analysis of breathing traveling motions appearing in heart muscles.

Free Research Field

非線形解析