2019-10-18T14:23:59Zhttps://eprints.lib.hokudai.ac.jp/dspace-oai/requestoai:eprints.lib.hokudai.ac.jp:2115/694792018-04-25T23:44:09Zhdl_2115_45007hdl_2115_116The convergence proof of the no-response test for localizing an inclusionNakamura, GenPotthast, RolandSini, Mourad410In 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 โยท (x)โ+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 โ @D at the boundary.Departmental Bulletin Paperapplication/pdfhttp://hdl.handle.net/2115/69479info:doi/10.14943/83825https://eprints.lib.hokudai.ac.jp/dspace/bitstream/2115/69479/1/pre674.pdfHokkaido University Preprint Series in Mathematics6741212004engpublisher