Study on inverse problems for partial differential equations using the probe and enclosure methods
| Project/Area Number |
21540162
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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 | Gunma University |
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Principal Investigator |
IKEHATA Masaru 群馬大学, 大学院・工学研究科, 教授 (90202910)
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| Co-Investigator(Renkei-kenkyūsha) |
ITOU Hiromichi 群馬大学, 大学院・工学研究科, 助教 (30400790)
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| Project Period (FY) |
2009 – 2012
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| Project Status |
Completed (Fiscal Year 2012)
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| Budget Amount *help |
¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000)
Fiscal Year 2012: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2011: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2010: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2009: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
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| Keywords | 境界値逆問題 / 波の物体散乱逆問題 / enclosure met hod / 熱方程式 / 波動方程式 / Helmholtz方程式 / 粘弾性体 / 逆散乱問題 / 囲い込み法 / 粘弾性体の方程式 / 解析学 / Enclosure method / Probe method / 熟方程式 / 複素幾何光学解 |
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| Research Abstract |
The most representative results obtained in this study consists of two parts. The first one shows that the enclosure method using dynamical data overa finite time interval can be applied to several inverse problems for the heat and waveequations and visco-elastic system of equations in three dimensions. And also the result raises several problems to be solved. The second one is the finding of the idea thatthe logarithmic differential of the indicator function in the enclosure method appliedto inverse obstacle scattering problems governed by the Helmholtz equation yieldsinformation two times more than the original indicator function.
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Report
(5 results)
Research Products
(56 results)
