Analysis of the nonlinear elliptic eigenvalue problems and inverse problems

2016 Fiscal Year Final Research Report

• Project/Area Number: 25400167
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Mathematical analysis
• Research Institution: Hiroshima University
• Principal Investigator: SHIBATA TETSUTARO 広島大学, 工学研究院, 教授 (90216010)
• Co-Investigator(Renkei-kenkyūsha): SAKAGUCHI SHIGERU 東北大学, 大学院情報科学研究科, 教授 (50215620) ; TANAKA KAZUNAGA 早稲田大学, 理工学術院, 教授 (20188288) ; KURATA KAZUHIRO 首都大学東京, 大学院理工学研究科, 教授 (10186489)
• Project Period (FY): 2013-04-01 – 2017-03-31
• Keywords: 関数方程式論 / 分岐曲線 / 漸近解析 / 固有値 / 逆問題 / 変分法

Outline of Final Research Achievements

In this study, we consider the inverse and direct bifurcation problems of nonlinear eigenvalue problems. For the direct problems, we establish the precise asymptotic formulas for the eigenvalue problems which have biological and physical background. For the inverse bifurcation problems, we consider the typical inverse problem for elliptic equations to understand well the structure of inverse problems. In particular, we concentrate on the study of the global structure of bifurcation curves for some nonlinear ordinary differential equations. We apply these precise asymptotic properties to the typical inverse bifurcation problem and obtained some fundamental and new results in this direction.

Free Research Field

数学解析