| Budget Amount *help |
¥4,680,000 (Direct Cost: ¥3,600,000、Indirect Cost: ¥1,080,000)
Fiscal Year 2018: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2017: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2016: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2015: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
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| Outline of Final Research Achievements |
I planned to investigate the structure of solutions on non-flat domains, on which the usual Pythagorean theorem does not hold and whose typical example is a sphere. The main aim of this research is to clarify the differences of the structures of solutions between on non-flat domains and on flat ones. First I investigated the structure of solutions to a nonlinear elliptic equation on a spherical cap and showed that the structure of solutions near bifurcating points is different from the flat case. Also, I investigated a linear parabolic equation having an inverse-square potential and showed the structure of stationary solutions and
the large-time behavior of the solution to the parabolic equation.
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