2010 Fiscal Year Final Research Report
On reconstruction problems in inverse problems of determining unknown coefficients for non-linear partial differential equations
| Project/Area Number |
20740078
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Single-year Grants |
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| Research Field |
Basic analysis
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| Research Institution | Tokyo University of Science |
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Principal Investigator |
WATANABE Michiyuki Tokyo University of Science, 人文社会・教育科学系, 准教授 (90374181)
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| Project Period (FY) |
2008 – 2010
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| Keywords | 偏微分方程式 / 散乱理論 / 逆問題 |
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| Research Abstract |
(1) We give the existence of outgoing eigen-function and its scattering amplitude for the two dimensional stationary wave equation with a friction term. We also prove in two dimensions that the friction coefficient is uniquely reconstructed from the scattering amplitude at a fixed low energy. (2) We study the inverse boundary value problem of determining a field-dependent coefficient for the non-linear wave equation in one space dimension. We prove that a linear part and a quadratic part of the field-dependent coefficient are uniquely reconstructed from the boundary measurements.
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