Analyses on layers arising in spatially inhomogeneous reaction diffusion equation

2015 Fiscal Year Final Research Report

• Project/Area Number: 24540207
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Global analysis
• Research Institution: Tokyo University of Marine Science and Technology
• Principal Investigator: Nakashima Kimie 東京海洋大学, その他部局等, 准教授 (10318800)
• Project Period (FY): 2012-04-01 – 2016-03-31
• Keywords: 非線形反応拡散方程式 / 特異摂動問題 / 遷移層

Outline of Final Research Achievements

We study a migration selction model for the solution of gene frequency, which is described by a spatially inhomogeneous reaction diffusion equation. We deal with this equation in one dimensional interval and assume that the diffusion coefficient is very small. We have constructed a steady state with many layers. This steady state is linearly stable. If there is any other nontrivial steady state `u'except for this layered steady-state, u stays close to a solution 0. Moreover, under some condition concerning to spatial inhomogeniety, this layered steady state is unique. We also study a migration selection model with integral term, and have succesfully constructed a layerd soution under the condition where diffusion term is very small.

Free Research Field

非線形解析