Geodesic
Some mathematical problems of atmospheric electricity
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh International Winter Mathematical School "Modern Methods of Function Theory and Related Problems", Voronezh, January 28 - February 2, 2021, Part 2, Tome 207 (2022), pp. 48-60

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In this paper, we discuss various formulations of mathematical problems arising in the description of the global electric circuit in the Earth's atmosphere. We consider initial-boundary-value problems for the nonstationary system of Maxwell equations, the system of Maxwell equations in the nonrelativistic electric approximation, and for the system of Maxwell equations in the quasistationary approximation generalizing the nonrelativistic electric and magnetic approximations.
Keywords: atmospheric electricity, global electric circuit, system of Maxwell equations, quasi-stationary approximation. 
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A. V. Kalinin; A. A. Tyukhtina. Some mathematical problems of atmospheric electricity. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh International Winter Mathematical School "Modern Methods of Function Theory and Related Problems", Voronezh, January 28 - February 2, 2021, Part 2, Tome 207 (2022), pp. 48-60. http://geodesic.mathdoc.fr/item/INTO_2022_207_a5/