{"title":"窄尾管域的特征值和散射频率","authors":"Rustem Gadyl'shin","doi":"10.1016/S1620-7742(01)01390-3","DOIUrl":null,"url":null,"abstract":"<div><p>The eigenvalue problem of the Dirichlet Laplacian in a singularly perturbed region, which is described as a bounded domain with a thin appendix is considered. The expansion of eigenvalues in the power series with respect to a small parameter (radius of the cross-section of the appendix) is constructed. This result is extended to the Helmholtz resonator with the finite thickness of a shell.</p></div>","PeriodicalId":100302,"journal":{"name":"Comptes Rendus de l'Académie des Sciences - Series IIB - Mechanics","volume":"329 10","pages":"Pages 723-726"},"PeriodicalIF":0.0000,"publicationDate":"2001-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/S1620-7742(01)01390-3","citationCount":"1","resultStr":"{\"title\":\"Eigenvalues and scattering frequencies for domains with narrow appendixes and tubes\",\"authors\":\"Rustem Gadyl'shin\",\"doi\":\"10.1016/S1620-7742(01)01390-3\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>The eigenvalue problem of the Dirichlet Laplacian in a singularly perturbed region, which is described as a bounded domain with a thin appendix is considered. The expansion of eigenvalues in the power series with respect to a small parameter (radius of the cross-section of the appendix) is constructed. This result is extended to the Helmholtz resonator with the finite thickness of a shell.</p></div>\",\"PeriodicalId\":100302,\"journal\":{\"name\":\"Comptes Rendus de l'Académie des Sciences - Series IIB - Mechanics\",\"volume\":\"329 10\",\"pages\":\"Pages 723-726\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2001-10-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1016/S1620-7742(01)01390-3\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Comptes Rendus de l'Académie des Sciences - Series IIB - Mechanics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S1620774201013903\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Comptes Rendus de l'Académie des Sciences - Series IIB - Mechanics","FirstCategoryId":"1085","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S1620774201013903","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Eigenvalues and scattering frequencies for domains with narrow appendixes and tubes
The eigenvalue problem of the Dirichlet Laplacian in a singularly perturbed region, which is described as a bounded domain with a thin appendix is considered. The expansion of eigenvalues in the power series with respect to a small parameter (radius of the cross-section of the appendix) is constructed. This result is extended to the Helmholtz resonator with the finite thickness of a shell.
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