Two sides of probe method and obstacle with impedance boundary condition
Abstract
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.
Cite
@article{arxiv.math/0611218,
title = {Two sides of probe method and obstacle with impedance boundary condition},
author = {Masaru Ikehata},
journal= {arXiv preprint arXiv:math/0611218},
year = {2010}
}
Comments
19pages