2017 Fiscal Year Annual Research Report
Inversion and prediction problems in anomalous diffusion
| Project/Area Number |
16H06712
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| Research Institution | The University of Tokyo |
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Principal Investigator |
李 志遠 東京大学, 大学院数理科学研究科, 特任研究員 (00782450)
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| Project Period (FY) |
2016-08-26 – 2018-03-31
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| Keywords | Caputo derivative / unique continuation / inverse problem |
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| Outline of Annual Research Achievements |
The anomalous diffusion processes were found in many problems in the fields of science and engineering. For the qualitative analysis of these problem, a macro-model named time-fractional diffusion equation with Caputo derivative is derived by using the continuous time random walk. We considered two kinds of inverse problem:
1. Unique continuation. By using Theta function method and Laplace transform argument, we proved a classical type unique continuation, say, the vanishment of a solution to a the fractional diffusion equation in an open subset implies its vanishment in the whole domain provided the solution vanishes on the whole boundary.
2. Inverse problem in determining the fractional order. By exploiting the integral equation of the solution u to the our problem, and carrying out the inversion Laplace transforms, we verified the Lipschitz continuous dependency of the fractional order with respect to the overposed data.
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| Research Progress Status |
29年度が最終年度であるため、記入しない。
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| Strategy for Future Research Activity |
29年度が最終年度であるため、記入しない。
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