Problems of Determining Quasi-Stationary Electromagnetic Fields in Weakly Inhomogeneous Media

Pub Date : 2024-07-18 DOI:10.1134/s0965542524700556
A. V. Kalinin, A. A. Tyukhtina, S. A. Malov
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Abstract

Formulations of initial-boundary value problems for the system of Maxwell’s equations in various quasi-stationary approximations in homogeneous and inhomogeneous conducting media are considered. In the case of weakly inhomogeneous media, asymptotic expansions of solutions to the considered initial-boundary value problems in a parameter characterizing the degree of inhomogeneity of the medium are formulated and substantiated. It is shown that the construction of an asymptotic expansion for the quasi-stationary electromagnetic approximation leads to successively solving independent problems for the quasi-stationary electric and quasi-stationary magnetic approximations in a homogeneous medium. Conditions for the initial data providing the convergence of the asymptotic series are given.

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弱不均匀介质中准静态电磁场的确定问题
摘要 研究了麦克斯韦方程组在均质和非均质导电介质中各种准静态近似的初始边界值问题。在弱非均质介质情况下,对所考虑的初界值问题的解的渐近展开进行了表述和论证,该参数表征了介质的非均质程度。研究表明,构建准稳态电磁近似的渐近展开,可以连续求解均质介质中准稳态电近似和准稳态磁近似的独立问题。给出了提供渐近级数收敛的初始数据条件。
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