On t-local solvability of inverse scattering problems in two-dimensional layered media

The solvability of two-dimensional inverse scattering problems for the Klein-Gordon equation and the Dirac system in a time-local formulation is analyzed in the framework of the Galerkin method. A necessary and sufficient condition for the unique solvability of these problems is obtained in the form...

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Bibliographic Details
Published in:Computational mathematics and mathematical physics 2015-06, Vol.55 (6), p.1033-1050
Main Author: Baev, A. V.
Format: Article
Language:English
Subjects:
Acoustics
Computational mathematics
Computational Mathematics and Numerical Analysis
Energy conservation
Energy conservation law
Galerkin methods
Geophysics
Inverse problems
Inverse scattering
Klein-Gordon equation
Mathematical analysis
Mathematical models
Mathematics
Mathematics and Statistics
Navier-Stokes equations
Physics
Scattering
Studies
Two dimensional
Velocity
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Summary:The solvability of two-dimensional inverse scattering problems for the Klein-Gordon equation and the Dirac system in a time-local formulation is analyzed in the framework of the Galerkin method. A necessary and sufficient condition for the unique solvability of these problems is obtained in the form of an energy conservation law. It is shown that the inverse problems are solvable only in the class of potentials for which the stationary Navier-Stokes equation is solvable.
ISSN:0965-5425
1555-6662
DOI:10.1134/S0965542515060032