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Darwin Approximation for the System of Maxwell’s Equations in Inhomogeneous Conducting Media

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Abstract

A quasi-stationary Darwin approximation for the system of Maxwell’s equations in inhomogeneous conducting media is studied. An existence and uniqueness theorem for the initial-boundary value problem for the resulting system of differential equations is proved. Estimates of the proximity between the solutions of the quasi-stationary problem under consideration and the corresponding nonstationary problem, depending on the characteristic values of the data, are presented.

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Funding

This work was supported by a grant from the Russian Science Foundation, project no. 18-77-10061.

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Authors and Affiliations

  1. Lobachevsky University, Mathematical Center, 603950, Nizhny Novgorod, Russia

    A. V. Kalinin & A. A. Tyukhtina

  2. Institute of Applied Physics, 603950, Nizhny Novgorod, Russia

    A. V. Kalinin

Authors
  1. A. V. Kalinin
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  2. A. A. Tyukhtina
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Correspondence to A. V. Kalinin or A. A. Tyukhtina.

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Translated by E. Chernokozhin

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Kalinin, A.V., Tyukhtina, A.A. Darwin Approximation for the System of Maxwell’s Equations in Inhomogeneous Conducting Media. Comput. Math. and Math. Phys. 60, 1361–1374 (2020). https://doi.org/10.1134/S0965542520080102

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