| Co-Investigator(Kenkyū-buntansha) |
川上 竜樹 龍谷大学, 理工学部, 教授 (20546147)
石渡 通徳 大阪大学, 基礎工学研究科, 教授 (30350458)
岡部 真也 東北大学, 理学研究科, 准教授 (70435973)
小川 卓克 東北大学, 理学研究科, 教授 (20224107)
小池 茂昭 東北大学, 理学研究科, 教授 (90205295)
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| Budget Amount *help |
¥41,340,000 (Direct Cost: ¥31,800,000、Indirect Cost: ¥9,540,000)
Fiscal Year 2019: ¥5,070,000 (Direct Cost: ¥3,900,000、Indirect Cost: ¥1,170,000)
Fiscal Year 2018: ¥7,800,000 (Direct Cost: ¥6,000,000、Indirect Cost: ¥1,800,000)
Fiscal Year 2017: ¥8,580,000 (Direct Cost: ¥6,600,000、Indirect Cost: ¥1,980,000)
Fiscal Year 2016: ¥10,140,000 (Direct Cost: ¥7,800,000、Indirect Cost: ¥2,340,000)
Fiscal Year 2015: ¥9,750,000 (Direct Cost: ¥7,500,000、Indirect Cost: ¥2,250,000)
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| Outline of Final Research Achievements |
We developed the arguments in geometric analysis and asymptotic analysis, and studied power concavity properties of solutions and singular phenomena such as blow-up phenomena. Furthermore, we established a new method to study asymptotic analysis which is applicable to fractional heat equations. More precisely, we studied the following topics:
(1) Power concavity of solutions; (2) Solvability of nonlinear elliptic equations with dynamical boundary conditions; (3) Initial trace of solutions to nonlinear diffusion equations; (4) Blow-up set for systems of nonlinear heat equations; (5) Asymptotic analysis for the heat equation with a potential and its applications; (6) Higher order asymptotic analysis for fractional heat equations.
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