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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2015, Volume 55, Number 6, Pages 1039–1057
DOI: https://doi.org/10.7868/S0044466915060046 (Mi zvmmf10225) 		 
This article is cited in 8 scientific papers (total in 8 papers)

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

A. V. Baev

Faculty of Physics, Moscow State University, Moscow, 119992, Russia
Full-text PDF (322 kB) Citations (8)
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DOI: https://doi.org/10.7868/S0044466915060046
Abstract: 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.
Key words: acoustic, Klein–Gordon, Schrödinger, Riccati, Navier–Stokes, Gelfand–Levitan, and Volterra equations, Dirac system, solvability of inverse scattering problems.
Received: 16.06.2014
Revised: 02.12.2014
English version:
Computational Mathematics and Mathematical Physics, 2015, Volume 55, Issue 6, Pages 1033–1050
DOI: https://doi.org/10.1134/S0965542515060032
Bibliographic databases:
Document Type: Article
UDC: 519.633.9
Language: Russian
Citation: A. V. Baev, “On $t$-local solvability of inverse scattering problems in two-dimensional layered media”, Zh. Vychisl. Mat. Mat. Fiz., 55:6 (2015), 1039–1057; Comput. Math. Math. Phys., 55:6 (2015), 1033–1050
Citation in format AMSBIB
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    • This publication is cited in the following 8 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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