Mathematical analysis of interfacial dynamics in non-periodic environments and its applications

2014 Fiscal Year Final Research Report

• Project/Area Number: 24540119
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: General mathematics (including Probability theory/Statistical mathematics)
• Research Institution: Kanazawa University
• Principal Investigator: NAKAMURA Ken-Ichi 金沢大学, 数物科学系, 准教授 (40293120)
• Co-Investigator(Kenkyū-buntansha): YAZAKI Shigetoshi 明治大学, 理工学部, 准教授 (00323874) ; ISHIWATA Tetsuya 芝浦工業大学, システム工学部, 准教授 (50334917) ; NAKAMURA Toshiko (OGIWARA Toshiko) 城西大学, 理学部, 准教授 (70316678)
• Co-Investigator(Renkei-kenkyūsha): MATANO Hiroshi 東京大学, 大学院数理科学研究科, 教授 (40126165)
• Research Collaborator: MATSUOKA Hikaru
• Project Period (FY): 2012-04-01 – 2015-03-31
• Keywords: 界面ダイナミクス / 進行波 / 移動境界問題

Outline of Final Research Achievements

In this research project, for understanding the mechanisms of complex spatio-temporal dynamics of interfaces in spatially non-periodic media or environments, we developed new mathematical methods including a general theory for the behavior of unbounded global orbits in a class of strongly monotone semiflows. Furthermore, for various problems on interfacial dynamics with variational structure such as mass conservation and energy dissipation, we proposed stable numerical schemes having the same characteristic properties as the original problems do.

Free Research Field

応用数学