2010 Fiscal Year Final Research Report
Investigations on structures of the solutions to nonlinear elliptic partial differential equations on the sphere.
| Project/Area Number |
19540224
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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 | Osaka Prefecture University |
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Principal Investigator |
KABEYA Yoshitsugu Osaka Prefecture University, 工学研究科, 教授 (70252757)
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| Project Period (FY) |
2007 – 2010
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| Keywords | 分岐理論 / 不完全分岐 / 球面上の微分方程式 / 楕円型偏微分方程式 / ホットスポット |
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| Research Abstract |
In this research period, I investigated the imperfect bifurcations on azimuthal solutions to a nonlinear elliptic equation when the domain covers almost the whole sphere and showed how the structure of bifurcations asymptotically looked like. As for the cases including non-azimuthal solutions, I obtained some results just before the end of the term. Also, as a related topics, I studies the behavior of solutions to a heat equation with a potential and showed that the time global behavior was governed by solutions to the stationary problem.
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