{"title":"渐近方法在曲线上不连续的静止解稳定性问题中的应用","authors":"A. Liubavin, Mingkang Ni","doi":"10.1134/s0965542524700519","DOIUrl":null,"url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>This article is considering the stability property of the solution with inner layer for singularly perturbed stationary equation with Neumann boundary conditions. The right-hand side is assumed to have discontinuity on some arbitrary curve <span>\\(h(t)\\)</span>. Stability analysis is performed by obtaining the first non-zero coefficient of the series for eigenvalue and eigenfunction from the Sturm–Liouville problem. Theory of the asymptotic approximations is used in order to construct them.</p>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-07-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Application of Asymptotic Methods to the Question of Stability in Stationary Solution with Discontinuity on a Curve\",\"authors\":\"A. Liubavin, Mingkang Ni\",\"doi\":\"10.1134/s0965542524700519\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<h3 data-test=\\\"abstract-sub-heading\\\">Abstract</h3><p>This article is considering the stability property of the solution with inner layer for singularly perturbed stationary equation with Neumann boundary conditions. The right-hand side is assumed to have discontinuity on some arbitrary curve <span>\\\\(h(t)\\\\)</span>. Stability analysis is performed by obtaining the first non-zero coefficient of the series for eigenvalue and eigenfunction from the Sturm–Liouville problem. Theory of the asymptotic approximations is used in order to construct them.</p>\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2024-07-18\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1134/s0965542524700519\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1134/s0965542524700519","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Application of Asymptotic Methods to the Question of Stability in Stationary Solution with Discontinuity on a Curve
Abstract
This article is considering the stability property of the solution with inner layer for singularly perturbed stationary equation with Neumann boundary conditions. The right-hand side is assumed to have discontinuity on some arbitrary curve \(h(t)\). Stability analysis is performed by obtaining the first non-zero coefficient of the series for eigenvalue and eigenfunction from the Sturm–Liouville problem. Theory of the asymptotic approximations is used in order to construct them.