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The convergence proof of the no-response test for localizing an inclusion
| Title: | The convergence proof of the no-response test for localizing an inclusion |
| Authors: | Nakamura, Gen Browse this author | | Potthast, Roland Browse this author | | Sini, Mourad Browse this author |
| Issue Date: | 2004 |
| Publisher: | Department of Mathematics, Hokkaido University |
| Journal Title: | Hokkaido University Preprint Series in Mathematics |
| Volume: | 674 |
| Start Page: | 1 |
| End Page: | 21 |
| Abstract: | In this paper, we use the no-response test idea, introduced in ([L-P], [P1]) for the inverse obstacle problem, to identify the interface of the discontinuity of the coefficient of the equation ∇· (x)∇+c(x) with piecewise regular and bounded function c(x). We use infinitely many Cauchy data as measurement and give a reconstructive method to localize the interface. We will base this multiwave version of the no-response test on two different proofs. The first one contains a pointwise estimate as used by the singular sources method. The second one is built on an energy (or an integral) estimate which is the basis of the probe method. As a conclusion of this, the no response can be seen as a unified framework for the probe and the singular sources method. As a further contribution, we provide a formula to reconstruct the values of the jump of (x), x ∈ @D at the boundary. |
| Type: | bulletin (article) |
| URI: | http://hdl.handle.net/2115/69479 |
| Appears in Collections: | 理学院・理学研究院 (Graduate School of Science / Faculty of Science) > Hokkaido University Preprint Series in Mathematics
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Submitter: 数学紀要登録作業用
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