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Inverse final observation problems for Maxwell’s equations in the quasi-stationary magnetic approximation and stable sequential Lagrange principles for their solving

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Abstract

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.

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Authors and Affiliations

  1. Nizhny Novgorod State University, Nizhny Novgorod, 603950, Russia

    A. V. Kalinin, M. I. Sumin & A. A. Tyukhtina

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  1. A. V. Kalinin
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  2. M. I. Sumin
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  3. A. A. Tyukhtina
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Correspondence to A. V. Kalinin.

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Original Russian Text © A.V. Kalinin, M.I. Sumin, A.A. Tyukhtina, 2017, published in Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki, 2017, Vol. 57, No. 2, pp. 187–209.

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Kalinin, A.V., Sumin, M.I. & Tyukhtina, A.A. Inverse final observation problems for Maxwell’s equations in the quasi-stationary magnetic approximation and stable sequential Lagrange principles for their solving. Comput. Math. and Math. Phys. 57, 189–210 (2017). https://doi.org/10.1134/S0965542517020075

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