{"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}
引用次数: 0
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.