| Project/Area Number |
26287020
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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| Allocation Type | Partial Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Mathematical analysis
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| Research Institution | Tohoku University |
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Principal Investigator |
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| Co-Investigator(Kenkyū-buntansha) |
倉田 和浩 首都大学東京, 理工学研究科, 教授 (10186489)
川上 竜樹 龍谷大学, 理工学部, 准教授 (20546147)
宮本 安人 東京大学, 大学院数理科学研究科, 准教授 (90374743)
池畠 優 広島大学, 工学(系)研究科(研究院), 教授 (90202910)
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| Co-Investigator(Renkei-kenkyūsha) |
ISHIGE Kazuhiro 東京大学, 大学院数理科学研究科, 教授 (90272020)
MIKAMI Toshio 津田塾大学, 学芸学部, 教授 (70229657)
MISAWA Masashi 熊本大学, 大学院自然科学研究科, 教授 (40242672)
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| Research Collaborator |
CAVALLINA Lorenzo 東北大学, 大学院情報科学研究科, D3
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| Project Period (FY) |
2014-04-01 – 2018-03-31
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| Project Status |
Completed (Fiscal Year 2017)
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| Budget Amount *help |
¥16,380,000 (Direct Cost: ¥12,600,000、Indirect Cost: ¥3,780,000)
Fiscal Year 2017: ¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000)
Fiscal Year 2016: ¥3,900,000 (Direct Cost: ¥3,000,000、Indirect Cost: ¥900,000)
Fiscal Year 2015: ¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000)
Fiscal Year 2014: ¥4,030,000 (Direct Cost: ¥3,100,000、Indirect Cost: ¥930,000)
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| Keywords | 熱拡散方程式 / 不変等温面 / 複合媒質 / 不変等熱流面 / 反応拡散方程式 / 半線形楕円型方程式 / 囲い込み法 / 逆問題 / 反応拡散系 / 物体内空洞逆問題 / 関数方程式論 / 解析学 / 幾何学 / 実関数論 / 数理物理 / 非線形シュレディンガー方程式 / アレンカーン型方程式 / 漸近展開理論 / 優臨界楕円型方程式 / 導電場方程式 / 中性導体 / 同心球 / 非線形放物型方程式 / エネルギー最小解 / 拡散方程式 / 円柱面 / 領域の幾何 / 国際研究者交流 / イタリア：スペイン：韓国 |
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| Outline of Final Research Achievements |
We studied mainly the relationship between the behavior of solutions and the geometry of domains in the problems widely described by partial differential equations from the point of view of inverse problems. First, the topology of unbounded stationary isothermic surfaces in Euclidean 3-space was completely determined, and the almost complete characterization of the hyperplanes and the circular cylinders involving a stationary isothermic surface was obtained. Secondly, in the conductivity equation over composite media in Euclidean 3-space, we succeeded in characterizing the concentric balls by means of the neutral conductors without any influence on outside uniform electric fields. Thirdly, in the heat equation over composite media we obtained the characterization of the concentric balls involving either a stationary isothermic surface or a surface with the constant heat flow property among two-phase heat conductors.
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