Two sides of probe method and obstacle with impedance boundary condition

Details Two sides of probe method and obstacle with impedance boundary condition Two sides of probe method and obstacle with impedance boundary condition

2006-11-08

arxiv.org/abs/math/0611218v1

Hokkaido Math. J., 35(2006), 659-681

Mathematics

Analysis of PDEs

19pages

Scientific paper

An inverse boundary value problem for the Helmholtz equation in a bounded domain is considered. The problem is to extract information about an unknown obstacle embedded in the domain with unknown impedance boundary condition (the Robin condition) from the associated Dirichlet-to-Neumann map. The main result is a characterization of the unknown obstacle via the sequences that are constructed by the Dirichlet-to-Neumann map, under smallness conditions on the wave number and the upper bound of the impedance. Moreover two alternative simple proofs of a previous result of Cheng-Liu-Nakamura which are based on only some energy estimates, an analysis of the blowup of the energy of so-called reflected solutions and an application of the enclosure method to the problem are also given.

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