| Budget Amount *help |
¥4,550,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥1,050,000)
Fiscal Year 2014: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
Fiscal Year 2013: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2012: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
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| Outline of Final Research Achievements |
We consider the following problems: (A) Dynamical aspects of geometric evolution equations defined on planar curves; (B) Obstacle problem for parabolic biharmonic equation. Regarding the theme (A), we proved that (A1) a planar open curve with infinite length converges to the borderline elastica as time goes to infinity; (A2) if a solution of geometric evolution equation converges to an equilibrium along a sequence of time, then the curve converges to an equilibrium as time goes to infinity, provided that the set of the equilibria has a discrete structure. Concerning the theme (B), we considered (B1) obstacle problem for the parabolic biharmonic equation, and (B2) two-obstacle problem for the parabolic biharmonic equation. For each problems (B1) and (B2), we proved the long time existence of solutions and investigated the regularity of the solutions.
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