| Budget Amount *help |
¥4,060,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥660,000)
Fiscal Year 2009: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2008: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2007: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2006: ¥1,200,000 (Direct Cost: ¥1,200,000)
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| Research Abstract |
To analyze crystal growth phenomena and image processing technology, various differential equations governing motion of curves or surfaces under a particular law are proposed. We focused on anisotropic curvature flow equations with very singular interfacial energy. We analyzed one of typical equations, so-called a crystalline curvature flow equation. For any initial polygon, we proved the well-posedness of the initial value problem of the corresponding system of ordinary differential equations by using self-similar solutions and a geometric method. On the other hand, we showed that the idea of singular interfacial energy is effective to mathematical analysis of shock waves. Meanwhile anisotropic curvature flow equations with inhomogeneous external force are important to understand crystal growth phenomena. We derived fundamental comparison principle of them.
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