| Project/Area Number |
14540207
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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 |
SHIBATA Tetsutaro Hiroshima University, Graduate School of Engineering, Professor, 大学院・工学研究科, 教授 (90216010)
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| Co-Investigator(Kenkyū-buntansha) |
YOSHIDA Kiyoshi Hiroshima University, Faculty of Integrated Arts and Sciences, Professor, 総合科学部, 教授 (80033893)
MIZUTA Yoshihiro Hiroshima University, Faculty of Integrated Arts and Sciences, Professor, 総合科学部, 教授 (00093815)
USAMI Hiroyuki Hiroshima University, Faculty of Integrated Arts and Sciences, Associate Professor, 総合科学部, 助教授 (90192509)
TANAKA Kazunaga Waseda University, School of Science and Engineering, Professor, 理工学術院, 教授 (20188288)
KURATA Kazuhiro Tokyo Metropolitan University, Graduate School of Science, Professor, 大学院・理学研究科, 教授 (10186489)
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| Project Period (FY) |
2002 – 2004
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| Project Status |
Completed (Fiscal Year 2004)
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| Budget Amount *help |
¥3,400,000 (Direct Cost: ¥3,400,000)
Fiscal Year 2004: ¥1,100,000 (Direct Cost: ¥1,100,000)
Fiscal Year 2003: ¥1,100,000 (Direct Cost: ¥1,100,000)
Fiscal Year 2002: ¥1,200,000 (Direct Cost: ¥1,200,000)
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| Keywords | Nonlinear / Eigenvalue / Asymptotic analysis / Variational methods / Singular perturbation / Boundary layer / Simple pendulum / Interior behavior / 変文法 |
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| Research Abstract |
We studied nonlinear elliptic eigenvalue problems with several parameters. Our main concern was to clarify the asymptotic properties of eigenvalue parameters and associated eigenfunctions by using variational methods and singular perturbation approaches when a parameter was very large.
We studied two-parameter ordinary differential equations with two pure power nonlinear terms. We established several asymptotic formulas for eigenvalues by using several variational approaches. We also studied the two-parameter problems which were related to the simple pendulum problems. We established the precise asymptotic formulas for the solutions with boundary layers when a parameter was very large under the Dirichlet boundary conditions. The formulas obtained here were totally different from those for the associated one-parameter simple pendulum problems.
For problems with one-parameter, we studied the problems which were related to the simple pendulum problems. We first studied ordinary differential equations and established precise asymptotic formulas for the boundary layers when a parameter was large under the Dirichlet boundary conditions. We next extended this result to the nonlinear elliptic eigenvalue problems in a smooth bounded domain. We studied nonlinear elliptic eigenvalue problems with pure power nonlinearity and established the asymptotic formula for the eigenvalues in L-2 framework. We also treated the perturbed simple pendulum problems in a bounded domain. It is known that if parameter is large, then an associated solution is nearly flat inside the domain. We have succeeded to establish the precise asymptotic formulas for the interior behavior of the solutions to understand precisely how flat the solutions were inside a domain when a parameter was very large. The formulas obtained here were exactly represented by using the nonlinear term.
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