2011 Fiscal Year Final Research Report
On a dynamics of a solution for geometric evolution equations with a variational structure
| Project/Area Number |
20740086
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Single-year Grants |
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| Research Field |
Global analysis
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| Research Institution | Muroran Institute of Technology |
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Principal Investigator |
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| Project Period (FY) |
2008 – 2011
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| Keywords | 表面拡散方程式 / 平均曲率一定曲面 / Willmore流方程式 / 平均曲率流方程式 |
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| Research Abstract |
The motion of three hypersurfaces by mean curvature flow is studied. These hypersurfaces intersect each other. The existence of a local-in-time solution to an initial and boundary value problem for a system of nonlinear parabolic partial differential equations with non-local term is showed. Also, the motion of an axisymmetric surface by surface diffusion equation is studied. In order to obtain the linearized stability of a stationary surface, a corresponding eigenvalue problem is derived and analyzed.
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