Mathematical analysis for the Lotka-Volterra system with nonlinear diffusion

2014 Fiscal Year Final Research Report

• Project/Area Number: 24740101
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Global analysis
• Research Institution: The University of Electro-Communications
• Principal Investigator: KOUSUKE Kuto 電気通信大学, 情報理工学(系)研究科, 准教授 (40386602)
• Project Period (FY): 2012-04-01 – 2015-03-31
• Keywords: 非線形拡散 / 数理生物学モデル / 楕円型方程式 / 分岐 / 極限系 / 移流 / 拡散の相互作用

Outline of Final Research Achievements

This research studied the global structure of stationary solutions to the Lotka-Volterra system with nonlinear diffusion. Among other things, this research focused on the limiting system as the nonlinear diffusion term tends to infinity, which characterizes the limiting behavior of stationary solutions, and derived the curve of the set of non-constant solutions to the limiting system (the global bifurcation curve) in a functional space. As an example of results, this research proved that an element of unknown functions blows up as a bifurcation parameter approaches the second eigenvalue of the Laplace operator.

Free Research Field

非線形偏微分方程式