Study on reaction-diffusion equations and related free boundary problems

2014 Fiscal Year Final Research Report

• Project/Area Number: 24540220
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Global analysis
• Research Institution: Waseda University
• Principal Investigator: YAMADA Yoshio 早稲田大学, 理工学術院, 教授 (20111825)
• Co-Investigator(Renkei-kenkyūsha): OTANI Mitsuharu 早稲田大学, 理工学術院, 教授 (30119656) ; TANAKA Kazunaga 早稲田大学, 理工学術院, 教授 (20188288) ; HIROSE Munemitsu 明治大学, 理工学部, 准教授 (50287984) ; NAKASHIMA Kimie 東京海洋大学, 海洋科学部, 准教授 (10318800) ; TAKEUCHI Shingo 芝浦工業大学, システム理工学部, 准教授 (00333021) ; KUTO Kousuke 電気通信大学, 情報理工学研究科, 准教授 (40386602) ; WAKASA Tohru 九州工業大学, 工学研究院, 准教授 (20454069) ; OEDA Kazuhiro 早稲田大学, グローバルエデュケーションセンター, 助教 (70580364)
• Research Collaborator: KANEKO Yuki
• Project Period (FY): 2012-04-01 – 2015-03-31
• Keywords: 反応拡散方程式 / 自由境界問題 / 数理生態学 / 非線形現象 / 正値定常解 / 非局所項

Outline of Final Research Achievements

This research is concerned with a free boundary problem for reaction-diffusion equations in mathematical ecology. This problem models the invasion or migration of a certain biological species. Our main interest is to study the evolution of the population density and habitat of the species. The population density is described by a reaction-diffusion equation and the boundary (or a part of the boundary) of the habitat is controlled by a free boundary condition of Stefan type. We could obtain theoretical understanding on asymptotic behaviors of solutions for free boundary problems of various types: whether the species vanishes eventually or the species persists with spreading free boundary. Moreover, we got precise results on the spreading speed of the free boundary.

Free Research Field

非線形微分方程式