A theoretical approach to constructing asymptotic solutions to reaction-diffusion systems

2014 Fiscal Year Final Research Report

• Project/Area Number: 24540216
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Global analysis
• Research Institution: University of Miyazaki
• Principal Investigator: MASATO Iida 宮崎大学, 工学教育研究部, 教授 (00242264)
• Co-Investigator(Kenkyū-buntansha): NINOMIYA Hirokazu 明治大学, 総合数理学部, 専任教授 (90251610)
• Co-Investigator(Renkei-kenkyūsha): TSUJIKAWA Tohru 宮崎大学, 工学教育研究部, 教授 (10258288)
• Project Period (FY): 2012-04-01 – 2015-03-31
• Keywords: 非線形解析 / 反応拡散系 / 漸近解

Outline of Final Research Achievements

In reaction-diffusion systems various shapes of solutions were observed by numerical simulations, however most of them have not rigorously been verified yet. Through this research much information, that will help us to construct asymptotic solutions approximating solutions with `corner layer' and solutions which describe `multi-stage invasion' in population dynamics, have been obtained as follows. (1)Some united viewpoints over several reaction-diffusion systems have been introduced, in order to describe the shapes and the structure of the solutions in their singular limits. The viewpoints will help us to decide whether corner layers do appear or not in some singular limits. (2)The global structure of `single waves' in the Fisher-KPP equation have been shown in collective known facts concerning their existence and stability. Asymptotic solutions which describe multi-stage invasion in cooperation-diffusion systems with many species will be constructed of these single waves.

Free Research Field

数学解析