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The convergence proof of the no-response test for localizing an inclusion

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Please use this identifier to cite or link to this item:http://doi.org/10.14943/83825

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
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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