Inverse final observation problems for Maxwell's equations in the quasi-stationary magnetic approximation and stable sequential Lagrange principles for their solving
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 57 (2017) no. 2, pp. 187-209
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An initial-boundary value problem for Maxwell's equations in the quasi-stationary magnetic approximation is investigated. Special gauge conditions are presented that make it possible to state the problem of independently determining the vector magnetic potential. The well-posedness of the problem is proved under general conditions on the coefficients. For quasi-stationary Maxwell equations, final observation problems formulated in terms of the vector magnetic potential are considered. They are treated as convex programming problems in a Hilbert space with an operator equality constraint. Stable sequential Lagrange principles are stated in the form of theorems on the existence of a minimizing approximate solution of the optimization problems under consideration. The possibility of applying algorithms of dual regularization and iterative dual regularization with a stopping rule is justified in the case of a finite observation error.
@article{ZVMMF_2017_57_2_a0,
author = {A. V. Kalinin and M. I. Sumin and A. A. Tyukhtina},
title = {Inverse final observation problems for {Maxwell's} equations in the quasi-stationary magnetic approximation and stable sequential {Lagrange} principles for their solving},
journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
pages = {187--209},
publisher = {mathdoc},
volume = {57},
number = {2},
year = {2017},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZVMMF_2017_57_2_a0/}
}
TY - JOUR AU - A. V. Kalinin AU - M. I. Sumin AU - A. A. Tyukhtina TI - Inverse final observation problems for Maxwell's equations in the quasi-stationary magnetic approximation and stable sequential Lagrange principles for their solving JO - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki PY - 2017 SP - 187 EP - 209 VL - 57 IS - 2 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/ZVMMF_2017_57_2_a0/ LA - ru ID - ZVMMF_2017_57_2_a0 ER -
%0 Journal Article %A A. V. Kalinin %A M. I. Sumin %A A. A. Tyukhtina %T Inverse final observation problems for Maxwell's equations in the quasi-stationary magnetic approximation and stable sequential Lagrange principles for their solving %J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki %D 2017 %P 187-209 %V 57 %N 2 %I mathdoc %U http://geodesic.mathdoc.fr/item/ZVMMF_2017_57_2_a0/ %G ru %F ZVMMF_2017_57_2_a0
A. V. Kalinin; M. I. Sumin; A. A. Tyukhtina. Inverse final observation problems for Maxwell's equations in the quasi-stationary magnetic approximation and stable sequential Lagrange principles for their solving. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 57 (2017) no. 2, pp. 187-209. http://geodesic.mathdoc.fr/item/ZVMMF_2017_57_2_a0/