2013 Fiscal Year Final Research Report
Analysis on singular behavior of interfaces by multiple interface dynamics
| Project/Area Number |
22740109
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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 | Gunma University |
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Principal Investigator |
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| Project Period (FY) |
2010-04-01 – 2014-03-31
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| Keywords | 界面の発展方程式 / 等高線法 / 曲率流方程式 / 粘性解 / 結晶成長 / 退化放物型方程式 / 反応拡散方程式 |
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| Research Abstract |
A level set method for evolving spirals by an eikonal-curvature equation on a crystal surface is studied. A level set equation for interlaced spiral is proposed and examined numerically. The stability of a bunch of spirals evolving with an eikonal-curvature equation is obtained. Growth rate of the crystal surface by a single or multiple spiral steps are estimated and examined numerically. Stationary solution to the level set equation with the situation of an inactive pair is obtained. A priori estimate for Lipschitz continuity of solutions to an approximating equation of the level set equation is obtained. A diffusion method for data separation is proposed as an application of the infinite propagation property on the heat equation.
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