Elucidation of phenomena in the higher dimensional domain applying the reduced system and construction of the mathematical method

2017 Fiscal Year Final Research Report

• Project/Area Number: 26400173
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Mathematical analysis
• Research Institution: University of Miyazaki
• Principal Investigator: Tsujikawa Tohru 宮崎大学, 工学部, 教授 (10258288)
• Co-Investigator(Renkei-kenkyūsha): KUTO Kousuke 電気通信大学, 情報理工学(系)研究科, 教授 (40386602) ; EI Shin-ichiro 北海道大学, 理学研究院, 教授 (30201362) ; SAKURAI Tatsunari 山口芸術短期大学, 芸術表現学科, 准教授 (60353322)
• Project Period (FY): 2014-04-01 – 2018-03-31
• Keywords: differential equation / bifurcation method / singular perturbation

Outline of Final Research Achievements

The study of Reaction-Diffusion Equation is important to elucidate the pattern formation. This research is to determine the global structure of nonconstant stationary solutions of Lotka-Volterra competition model, which describes the population dynamics of some biology. Under Neumann boundary condition, we show the sufficient condition of the existence of nonconstant solutions for coefficient parameters by Leray-Shauder degree theory. On the other hand, we know that the solution structure is complex by numerical computations. In order to show the global solution structure, we introduce a limiting system by using some reduction to the model equation. It is a scalar equation with an integral constraint. Since the solution structure of this scalar equation is well known by the bifurcation theory, we obtain the global solution structure due to solve the integral constraint by using Levelset analysis.

Free Research Field

応用数学