475 research outputs found
Some Results on Inverse Scattering
A review of some of the author's results in the area of inverse scattering is
given. The following topics are discussed: 1) Property and applications, 2)
Stable inversion of fixed-energy 3D scattering data and its error estimate, 3)
Inverse scattering with ''incomplete`` data, 4) Inverse scattering for
inhomogeneous Schr\"odinger equation, 5) Krein's inverse scattering method, 6)
Invertibility of the steps in Gel'fand-Levitan, Marchenko, and Krein inversion
methods, 7) The Newton-Sabatier and Cox-Thompson procedures are not inversion
methods, 8) Resonances: existence, location, perturbation theory, 9) Born
inversion as an ill-posed problem, 10) Inverse obstacle scattering with
fixed-frequency data, 11) Inverse scattering with data at a fixed energy and a
fixed incident direction, 12) Creating materials with a desired refraction
coefficient and wave-focusing properties.Comment: 24p
Invisible obstacles
It is proved that one can choose a control function on an arbitrary small
open subset of the boundary of an obstacle so that the total radiation from
this obstacle for a fixed direction of the incident plane wave and for a fixed
wave number will be as small as one wishes. The obstacle is called "invisible"
in this case
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