{"title":"Holomorphic Regularization of Singularly Perturbed Integro-Differential Equations","authors":"V. S. Besov, V. I. Kachalov","doi":"10.1134/s0012266124010014","DOIUrl":null,"url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> S.A. Lomov’s regularization method has long been used to solve integro-differential\nsingularly perturbed equations, which are very important from the viewpoint of applications. In\nthis method, the series in powers of a small parameter representing the solutions of these\nequations converge asymptotically. However, in accordance with the main concept of the method,\nto construct a general singular perturbation theory one must indicate conditions for the ordinary\nconvergence of these series. This is the subject of the present paper.\n</p>","PeriodicalId":50580,"journal":{"name":"Differential Equations","volume":"5 1","pages":""},"PeriodicalIF":0.8000,"publicationDate":"2024-04-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Differential Equations","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1134/s0012266124010014","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
S.A. Lomov’s regularization method has long been used to solve integro-differential
singularly perturbed equations, which are very important from the viewpoint of applications. In
this method, the series in powers of a small parameter representing the solutions of these
equations converge asymptotically. However, in accordance with the main concept of the method,
to construct a general singular perturbation theory one must indicate conditions for the ordinary
convergence of these series. This is the subject of the present paper.
期刊介绍：
Differential Equations is a journal devoted to differential equations and the associated integral equations. The journal publishes original articles by authors from all countries and accepts manuscripts in English and Russian. The topics of the journal cover ordinary differential equations, partial differential equations, spectral theory of differential operators, integral and integral–differential equations, difference equations and their applications in control theory, mathematical modeling, shell theory, informatics, and oscillation theory. The journal is published in collaboration with the Department of Mathematics and the Division of Nanotechnologies and Information Technologies of the Russian Academy of Sciences and the Institute of Mathematics of the National Academy of Sciences of Belarus.
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