{"title":"Problems of Determining Quasi-Stationary Electromagnetic Fields in Weakly Inhomogeneous Media","authors":"A. V. Kalinin, A. A. Tyukhtina, S. A. Malov","doi":"10.1134/s0965542524700556","DOIUrl":null,"url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>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.</p>","PeriodicalId":55230,"journal":{"name":"Computational Mathematics and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":0.7000,"publicationDate":"2024-07-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Computational Mathematics and Mathematical Physics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1134/s0965542524700556","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
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.
期刊介绍：
Computational Mathematics and Mathematical Physics is a monthly journal published in collaboration with the Russian Academy of Sciences. The journal includes reviews and original papers on computational mathematics, computational methods of mathematical physics, informatics, and other mathematical sciences. The journal welcomes reviews and original articles from all countries in the English or Russian language.
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