Two sides of probe method and obstacle with impedance boundary condition
IKEHATA, Masaru
Hokkaido Math. J., Tome 35 (2006) no. 1, p. 659-681 / Harvested from Project Euclid
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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.
Publié le : 2006-08-15
Classification:  inverse obstacle scattering problem,  probe method,  Poincar\'e inequality, enclosure method,  impedance boundary condition,  blowup,  obstacle,  indicator function,  35R30 
@article{1285766423,
     author = {IKEHATA, Masaru},
     title = {Two sides of probe method and obstacle with impedance boundary condition},
     journal = {Hokkaido Math. J.},
     volume = {35},
     number = {1},
     year = {2006},
     pages = { 659-681},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1285766423}
}

IKEHATA, Masaru. Two sides of probe method and obstacle with impedance boundary condition. Hokkaido Math. J., Tome 35 (2006) no. 1, pp.  659-681. http://gdmltest.u-ga.fr/item/1285766423/