Study of partial differential equations and tomography by microlocal and discrete methods
| Project/Area Number |
20540157
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Basic analysis
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| Research Institution | Ochanomizu University |
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Principal Investigator |
KANEKO Akira お茶の水女子大学, 名誉教授 (30011654)
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| Project Period (FY) |
2008 – 2011
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| Project Status |
Completed (Fiscal Year 2011)
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| Budget Amount *help |
¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000)
Fiscal Year 2011: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2010: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2009: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2008: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
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| Keywords | 代数解析 / 偏微分方程式 / トモグラフィー / 半線型熱方程式 / 藤田現象 / 爆発の臨界指数 / 2方向投影データトモグラフィ / 電荷分布の形状同定 / 解の爆発 / トモグラフィ / 逆問題 / 電荷分布の同定 / ニュートン法 / Fredholm型積分方程式 / f半線型熱方程式 / 離散トモグラフィ / 電荷分布の逆問題 / 解の爆発の臨界指数 / スイッチンググラフ |
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| Research Abstract |
We studied on various problems of partial differential equations and tomography by means of microlocal and discrete approach. Especially we got new interesting results on the critical exponent of blowup of semilinear heat equation with logarithmic nonlinearity by determining the critical exponent for generalized paraboloidal domain, and on the switching graph of solution sets of 2 projection tomography which is a means of studying non-uniqueness of solution, by enumerating them up to order 20 with aid of theoretical consideration and computer experiment.
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Report
(6 results)
Research Products
(27 results)
