{"title":"一个电物理方程的研究","authors":"V.V. Dyakin, V.Ya. Rayevskii","doi":"10.1016/0041-5553(90)90031-M","DOIUrl":null,"url":null,"abstract":"<div><p>The vector integral equation <span><span><span><math><mtext>αM+▿ </mtext><mtext>∫</mtext><mtext>ω</mtext><mtext>M▿|ξ−y|</mtext><msup><mi></mi><mn>−1</mn></msup><mtext> dy=H, α⩾0, ω⊂</mtext><mtext>R</mtext><msup><mi></mi><mn>3</mn></msup></math></span></span></span>, encountered in classical problems of electrostatics and magnetostatics, is investigated. The structure and properties of its solutions are investigated by studying the corresponding integral operator, and a numerical method is proposed.</p></div>","PeriodicalId":101271,"journal":{"name":"USSR Computational Mathematics and Mathematical Physics","volume":"30 1","pages":"Pages 213-217"},"PeriodicalIF":0.0000,"publicationDate":"1990-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/0041-5553(90)90031-M","citationCount":"2","resultStr":"{\"title\":\"Investigation of an equation of electrophysics\",\"authors\":\"V.V. Dyakin, V.Ya. Rayevskii\",\"doi\":\"10.1016/0041-5553(90)90031-M\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>The vector integral equation <span><span><span><math><mtext>αM+▿ </mtext><mtext>∫</mtext><mtext>ω</mtext><mtext>M▿|ξ−y|</mtext><msup><mi></mi><mn>−1</mn></msup><mtext> dy=H, α⩾0, ω⊂</mtext><mtext>R</mtext><msup><mi></mi><mn>3</mn></msup></math></span></span></span>, encountered in classical problems of electrostatics and magnetostatics, is investigated. The structure and properties of its solutions are investigated by studying the corresponding integral operator, and a numerical method is proposed.</p></div>\",\"PeriodicalId\":101271,\"journal\":{\"name\":\"USSR Computational Mathematics and Mathematical Physics\",\"volume\":\"30 1\",\"pages\":\"Pages 213-217\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1990-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1016/0041-5553(90)90031-M\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"USSR Computational Mathematics and Mathematical Physics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/004155539090031M\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"USSR Computational Mathematics and Mathematical Physics","FirstCategoryId":"1085","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/004155539090031M","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 2
摘要
研究了在静电学和静磁学经典问题中遇到的向量积分方程α m +±∫ω m |ξ−y|−1 dy=H， α≠0，ω∧R3。通过研究相应的积分算子，研究了其解的结构和性质，并提出了一种数值方法。
The vector integral equation , encountered in classical problems of electrostatics and magnetostatics, is investigated. The structure and properties of its solutions are investigated by studying the corresponding integral operator, and a numerical method is proposed.
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