Comparison between solutions of the Maxwell system of equations and its quasi-stationary approximation

Article type: Research Article

Authors: Galanin, Michail

Affiliations: Keldysh Institute of Applied Mathematics, 125047 Moscow, Miusskaja Sq.4, USSR

Abstract: Models for determining the electromagnetic fields are considered. The models consist of system of the Maxwell equations in the complete form and in the quasi-stationary approximation. Using the quasi-stationary approximation in media containing nonconducting subdomains is non correct from the physical point of view and give rise to a number of additional mathematical problems. The solutions of the Maxwell equations in the complete form and in the quasi-stationary approximation are compared. Initial boundary value problems are considered for conducting, nonconducting and mixed media. The conditions ensuring the closeness of solutions are established. The estimates are obtained in terms of input data of the problem. In particular, it has been proved that as the ratio of the characteristic rate to the light velocity tends to zero the strength of electric field in the conducting part and the strength of magnetic field in the entire domain, corresponding to the complete problem, converge to the ones corresponding to the approximate problem.

Keywords: Maxwell equations, quasi-stationary approximation

DOI: 10.3233/INF-1991-2304

Journal: Informatica, vol. 2, no. 3, pp. 378-402, 1991