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.

Keywords

Maxwell’s equations in quasi-stationary magnetic approximation vector potential gauge conditions inverse final observation problem retrospective inverse problem convex programming Lagrange principle dual regularization iterative dual regularization stopping rule 

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Copyright information

© Pleiades Publishing, Ltd. 2017

Authors and Affiliations

  • A. V. Kalinin
    • 1
  • M. I. Sumin
    • 1
  • A. A. Tyukhtina
    • 1
  1. 1.Nizhny Novgorod State UniversityNizhny NovgorodRussia

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