{"title":"奇异摄动抛物型问题在临界情况下解的渐近性质","authors":"V.Yu. Buchnev","doi":"10.1016/0041-5553(90)90204-6","DOIUrl":null,"url":null,"abstract":"<div><p>A zeroth-order boundary-layer asymptotic expansion is constructed and proved for solving a mixed boundary-value problem for a parabolic equation in the critical case. A smoothing procedure is applied to the nonsmooth terms of the asymptotic expansion when constructing the solution.</p></div>","PeriodicalId":101271,"journal":{"name":"USSR Computational Mathematics and Mathematical Physics","volume":"30 3","pages":"Pages 154-161"},"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)90204-6","citationCount":"0","resultStr":"{\"title\":\"Asymptotic behaviour of the solution of the singularly perturbed parabolic problem in the critical case\",\"authors\":\"V.Yu. Buchnev\",\"doi\":\"10.1016/0041-5553(90)90204-6\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>A zeroth-order boundary-layer asymptotic expansion is constructed and proved for solving a mixed boundary-value problem for a parabolic equation in the critical case. A smoothing procedure is applied to the nonsmooth terms of the asymptotic expansion when constructing the solution.</p></div>\",\"PeriodicalId\":101271,\"journal\":{\"name\":\"USSR Computational Mathematics and Mathematical Physics\",\"volume\":\"30 3\",\"pages\":\"Pages 154-161\"},\"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)90204-6\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"USSR Computational Mathematics and Mathematical Physics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/0041555390902046\",\"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/0041555390902046","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Asymptotic behaviour of the solution of the singularly perturbed parabolic problem in the critical case
A zeroth-order boundary-layer asymptotic expansion is constructed and proved for solving a mixed boundary-value problem for a parabolic equation in the critical case. A smoothing procedure is applied to the nonsmooth terms of the asymptotic expansion when constructing the solution.
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