Two sides of probe method and obstacle with impedance boundary condition.
Hokkaido Mathematical Journal, 35 (2006) pp.659-681
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 Dirichletto- 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.
|Uncontrolled Keywords||inverse obstacle scattering problem, probe method, Poincar\'e inequality, enclosure method, impedance boundary condition, blowup, obstacle, indicator function|