| Budget Amount *help |
¥3,250,000 (Direct Cost: ¥2,500,000、Indirect Cost: ¥750,000)
Fiscal Year 2015: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2014: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2013: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
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| Outline of Final Research Achievements |
We study the singular limit problem for the Allen-Cahn equation with Neumann boundary conditions and prove that associated energy measure converges to a measure theoretic solution of the mean curvature flow with right-angle boundary conditions. In particular, we establish the right-angle boundary condition in geometric measure theory and prove the boundary monotonicity formula for the energy measure.
Next, we study the mean curvature flow of graphs both with Neumann boundary conditions and transport terms. We derive a priori boundary gradient estimate for solutions and then show time local existence of solutions of the mean curvature flow under the natural assumption from the point of scaling arguments for the transport terms.
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