2012 Fiscal Year Final Research Report
Qualitative properties for the Laplace equation with a dynamical boundary condition
| Project/Area Number |
23654060
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| Research Category |
Grant-in-Aid for Challenging Exploratory Research
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| Allocation Type | Multi-year Fund |
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| Research Field |
Global analysis
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| Research Institution | Tohoku University |
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Principal Investigator |
ISHIGE Kazuhiro 東北大学, 大学院・理学研究科, 教授 (90272020)
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| Project Period (FY) |
2011 – 2012
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| Keywords | 動的境界条件 / ラプラス方程式 / ポアソン核 |
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| Research Abstract |
We studied the large time behavior of positive solutions for the Laplace equation with a nonlinear dynamical boundary condition and for a nonlinear elliptic equation with a dynamical boundary condition, in a half space. We identified a critical exponent for the global existence of positive solutions and showed that small solutions behave likesuitable multiples of the Poisson kernel.
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