| Budget Amount *help |
¥3,900,000 (Direct Cost: ¥3,000,000、Indirect Cost: ¥900,000)
Fiscal Year 2011: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2010: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2009: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
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| Research Abstract |
The summary of our results are stated as follows :(1)We prove that there exists a critical point of the variational problem for a certain space-time functional defined on planar curves which is concerned with stochastically perturbed mean curvature flow for curves ; (2)we show that, for a planar smooth non-closed curve with finite or infinite length, there exists a smooth solution of the steepest descent flow for the modified total squared curvature for any finite time. Moreover, we prove that, for an initial curve perturbed from line segment, the solution smoothly converges to a stationary solution along a certain sequence of time.
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