2016 Fiscal Year Final Research Report
On the geometric evolution equations described by the 4th order parabolic partial differential equations
| Project/Area Number |
24540200
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Global analysis
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| Research Institution | Kobe University (2014-2016)
Muroran Institute of Technology (2012-2013) |
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Principal Investigator |
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| Project Period (FY) |
2012-04-01 – 2017-03-31
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| Keywords | 表面拡散方程式 / ドロネー曲面 / 楕円積分 |
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| Outline of Final Research Achievements |
The geometric evolution equations described by the 4th order parabolic partial differential equations are studied. In particular, we focus on the surface diffusion equation and analyze the stability of the steady states for it. The surface diffusion equation has a variational structure that the area of the moving surface governed by this equation decreases whereas the volume of the region enclosed by its surface is preserved. This implies that the steady states are the constant mean curvature surfaces. In this project, we consider the axisymmetric constant mean curvature surfaces to be as the steady states for the surface diffusion equation and derive the criteria of the stability for them.
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| Free Research Field |
曲面の発展方程式
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