| Project/Area Number |
16K05232
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (C)
|
| Allocation Type | Multi-year Fund |
|---|
| Section | 一般 |
|---|
| Research Field |
Mathematical analysis
|
|---|
| Research Institution | Hiroshima University |
|---|
Principal Investigator |
|
|---|
| Project Period (FY) |
2016-04-01 – 2019-03-31
|
| Project Status |
Completed (Fiscal Year 2018)
|
| Budget Amount *help |
¥4,550,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥1,050,000)
Fiscal Year 2018: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2017: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2016: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
|
|---|
| Keywords | 時間依存型逆問題 / 複数種の波 / 囲い込み法 / 空洞推定 / 介在物推定 / 光学的距離 / 接合境界条件 / 二層問題 / 境界値逆問題 / 波源推定逆問題 |
|---|
| Outline of Final Research Achievements |
A medium with the flat transmission boundary which is the most fundamental setup in the wave motion phenomena in which several kinds of waves appear is considered. The inverse problem of estimating the unknown inclusions in the lower part of the transmission boundary by observing reflected waves for incident waves from the upper part is investigated through the asymptotic analysis of a resorvent. When propagation speed in the upper part is slower than that in the lower part, the reflective wave by inclusions is only refracted in the transmission boundary. Hence, the optical distance between inclusions and the set which takes observational data is obtained.
In the opposite case, the total reflection phenomena occur. According to these phenomena, the optical distance for two points may change, but the case of the usual refraction wave becomes the shortest also in this case. Hence, the same conclusion as the case where total reflection phenomena do not occur is obtained.
|
| Academic Significance and Societal Importance of the Research Achievements |
この問題はいわゆるレーダー探査問題の原型で、それを数学として何処まで定式化可能かについてある程度の解答を与えたものと考えられる。但し、指数減衰する関数を使用するため、実用については未知で、数値計算に限っても課題が残る。数学的な観点からは、完全に正しいことが保証され、先行研究を見ればこの結果を元により詳しい情報も導き出せる可能性が予想される。研究手法は主にレゾルベントの漸近挙動の解析に帰着し、「最短の距離（本研究では時間）」を得ることになる。この解析は1960年代から盛んに研究さている熱方程式の短時間漸近挙動と密接な関連があり、見た目は異なるこれらの問題の関連が明らかになった点にも意義がある。
|
