On $t$-local solvability of inverse scattering problems in two-dimensional layered media
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 55 (2015) no. 6, pp. 1039-1057
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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.
@article{ZVMMF_2015_55_6_a11,
author = {A. V. Baev},
title = {On $t$-local solvability of inverse scattering problems in two-dimensional layered media},
journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
pages = {1039--1057},
publisher = {mathdoc},
volume = {55},
number = {6},
year = {2015},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZVMMF_2015_55_6_a11/}
}
TY - JOUR AU - A. V. Baev TI - On $t$-local solvability of inverse scattering problems in two-dimensional layered media JO - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki PY - 2015 SP - 1039 EP - 1057 VL - 55 IS - 6 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/ZVMMF_2015_55_6_a11/ LA - ru ID - ZVMMF_2015_55_6_a11 ER -
%0 Journal Article %A A. V. Baev %T On $t$-local solvability of inverse scattering problems in two-dimensional layered media %J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki %D 2015 %P 1039-1057 %V 55 %N 6 %I mathdoc %U http://geodesic.mathdoc.fr/item/ZVMMF_2015_55_6_a11/ %G ru %F ZVMMF_2015_55_6_a11
A. V. Baev. On $t$-local solvability of inverse scattering problems in two-dimensional layered media. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 55 (2015) no. 6, pp. 1039-1057. http://geodesic.mathdoc.fr/item/ZVMMF_2015_55_6_a11/