{"title":"线性输运方程解的广义特征向量展开式","authors":"S. Charfi, A. Intissar, A. Jeribi","doi":"10.1080/00411450903404796","DOIUrl":null,"url":null,"abstract":"This article considers a time-dependent rectilinear transport equation that was first studied in B. Montagnini and V. Pierpaoli (Transport Theory and Statistical Physics 1(1) (1971) 59–75). The associated transport operator is the infinitesimal generator of a C 0-semigroup, its spectrum is discrete, and there are only finitely many eigenvalues in each vertical strip. We show that the C 0-semigroup can be expanded by its generalized eigenvectors, and we assert its differentiability.","PeriodicalId":49420,"journal":{"name":"Transport Theory and Statistical Physics","volume":"38 1","pages":"330 - 345"},"PeriodicalIF":0.0000,"publicationDate":"2009-11-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/00411450903404796","citationCount":"7","resultStr":"{\"title\":\"Expansion of Solution in Terms of Generalized Eigenvectors for a Rectilinear Transport Equation\",\"authors\":\"S. Charfi, A. Intissar, A. Jeribi\",\"doi\":\"10.1080/00411450903404796\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"This article considers a time-dependent rectilinear transport equation that was first studied in B. Montagnini and V. Pierpaoli (Transport Theory and Statistical Physics 1(1) (1971) 59–75). The associated transport operator is the infinitesimal generator of a C 0-semigroup, its spectrum is discrete, and there are only finitely many eigenvalues in each vertical strip. We show that the C 0-semigroup can be expanded by its generalized eigenvectors, and we assert its differentiability.\",\"PeriodicalId\":49420,\"journal\":{\"name\":\"Transport Theory and Statistical Physics\",\"volume\":\"38 1\",\"pages\":\"330 - 345\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2009-11-24\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1080/00411450903404796\",\"citationCount\":\"7\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Transport Theory and Statistical Physics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1080/00411450903404796\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Transport Theory and Statistical Physics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1080/00411450903404796","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Expansion of Solution in Terms of Generalized Eigenvectors for a Rectilinear Transport Equation
This article considers a time-dependent rectilinear transport equation that was first studied in B. Montagnini and V. Pierpaoli (Transport Theory and Statistical Physics 1(1) (1971) 59–75). The associated transport operator is the infinitesimal generator of a C 0-semigroup, its spectrum is discrete, and there are only finitely many eigenvalues in each vertical strip. We show that the C 0-semigroup can be expanded by its generalized eigenvectors, and we assert its differentiability.
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