| Budget Amount *help |
¥3,120,000 (Direct Cost: ¥2,400,000、Indirect Cost: ¥720,000)
Fiscal Year 2016: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2015: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2014: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
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| Outline of Final Research Achievements |
Concerning systems of linear analytic partial differential equations, we succeeded in giving coordinate-free formulations of the initial-boundary value mixed problems for D_X modules. At the same time we obtained a key theorem on the estimate of micro-supports of some holomorphic solution sheaf complexes in the sense of M.Kashiwara-P.Schapira, which is an essential tool clarifying the propagation of micro-analyticity of Sato hyperfunction solutions along the boundary. Concerning non-linear differential equations, we succeeded in clarifying the generalized eigenfunction expansions due to Hayato Chiba's theory on Kuramoto's weakly coupled many oscillators model on a circle for resonance phenomena. We found some essential error in Chiba's theory and gave a correct formulation and a proof.
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