{"title":"n 维空间中拉夫伦特埃夫积分方程解法的唯一性","authors":"M. M. Kokurin, V. V. Klyuchev, A. V. Gavrilova","doi":"10.1134/s0965542524030084","DOIUrl":null,"url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>We study the multidimensional analogue of the Lavrent’ev integral equation to which an inverse problem of acoustic sounding is reduced. Conditions under which the studied equation has a unique solution are established. Results of numerical experiments concerning the solution of the inverse acoustic problem with variously located sets of sources and detectors are presented.</p>","PeriodicalId":55230,"journal":{"name":"Computational Mathematics and Mathematical Physics","volume":"76 1","pages":""},"PeriodicalIF":0.7000,"publicationDate":"2024-04-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Uniqueness of a Solution to the Lavrent’ev Integral Equation in n-Dimensional Space\",\"authors\":\"M. M. Kokurin, V. V. Klyuchev, A. V. Gavrilova\",\"doi\":\"10.1134/s0965542524030084\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<h3 data-test=\\\"abstract-sub-heading\\\">Abstract</h3><p>We study the multidimensional analogue of the Lavrent’ev integral equation to which an inverse problem of acoustic sounding is reduced. Conditions under which the studied equation has a unique solution are established. Results of numerical experiments concerning the solution of the inverse acoustic problem with variously located sets of sources and detectors are presented.</p>\",\"PeriodicalId\":55230,\"journal\":{\"name\":\"Computational Mathematics and Mathematical Physics\",\"volume\":\"76 1\",\"pages\":\"\"},\"PeriodicalIF\":0.7000,\"publicationDate\":\"2024-04-22\",\"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/s0965542524030084\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Computational Mathematics and Mathematical Physics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1134/s0965542524030084","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
Uniqueness of a Solution to the Lavrent’ev Integral Equation in n-Dimensional Space
Abstract
We study the multidimensional analogue of the Lavrent’ev integral equation to which an inverse problem of acoustic sounding is reduced. Conditions under which the studied equation has a unique solution are established. Results of numerical experiments concerning the solution of the inverse acoustic problem with variously located sets of sources and detectors are presented.
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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