2012 Fiscal Year Final Research Report
Asymptotic analysis and inverse problems of the nonlinear elliptic eigenvalue problems
| Project/Area Number |
21540219
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Global analysis
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| Research Institution | Hiroshima University |
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Principal Investigator |
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| 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)
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| Project Period (FY) |
2009 – 2012
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| Keywords | 関数方程式論 / 固有値 / 漸近解析 / 変分法 / 逆問題 |
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| Research Abstract |
In this study, we investigated the precise asymptotic properties of the eigenfunctions and eigenvalues of nonlinear elliptic equations, and studied the inverse eigenvalue problems associated with thedirect problems. We clarify the global and local structures of the bifurcation curves for the equations with several types of nonlinear terms. As for inverse problems, we mainly studied the inverse bifurcation problems for logistic type equations. By using the theory of ordinary differential equations and the asymptotic expansion formulas for bifurcation curves, we determined the unknown nonlinear terms by the asymptotic behaviors of the bifurcation curves.
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