open access

https://doi.org/10.14943/83825

https://hdl.handle.net/2115/69479

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

英語

2004

Department of Mathematics, Hokkaido University

Hokkaido University Preprint Series in Mathematics

674

1-21

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.

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