{"title":"弱耦合系统的间接边界可观测性","authors":"Fatiha Alabau","doi":"10.1016/S0764-4442(01)02076-6","DOIUrl":null,"url":null,"abstract":"<div><p>This work is concerned with the indirect boundary observability of a coupled system of two wave equations. We show that for a sufficiently large time, the observation of the trace of the normal derivative of the first component of the solution on a part of the boundary allows us to get back a weakened energy of the initial data, this if the coupling parameter is sufficiently small, but non vanishing. This result leads to a new uniqueness theorem and also to an indirect exact controllability result.</p></div>","PeriodicalId":100300,"journal":{"name":"Comptes Rendus de l'Académie des Sciences - Series I - Mathematics","volume":"333 7","pages":"Pages 645-650"},"PeriodicalIF":0.0000,"publicationDate":"2001-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/S0764-4442(01)02076-6","citationCount":"26","resultStr":"{\"title\":\"Observabilité frontière indirecte de systèmes faiblement couplés\",\"authors\":\"Fatiha Alabau\",\"doi\":\"10.1016/S0764-4442(01)02076-6\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>This work is concerned with the indirect boundary observability of a coupled system of two wave equations. We show that for a sufficiently large time, the observation of the trace of the normal derivative of the first component of the solution on a part of the boundary allows us to get back a weakened energy of the initial data, this if the coupling parameter is sufficiently small, but non vanishing. This result leads to a new uniqueness theorem and also to an indirect exact controllability result.</p></div>\",\"PeriodicalId\":100300,\"journal\":{\"name\":\"Comptes Rendus de l'Académie des Sciences - Series I - Mathematics\",\"volume\":\"333 7\",\"pages\":\"Pages 645-650\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2001-10-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1016/S0764-4442(01)02076-6\",\"citationCount\":\"26\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Comptes Rendus de l'Académie des Sciences - Series I - Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0764444201020766\",\"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 I - Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0764444201020766","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Observabilité frontière indirecte de systèmes faiblement couplés
This work is concerned with the indirect boundary observability of a coupled system of two wave equations. We show that for a sufficiently large time, the observation of the trace of the normal derivative of the first component of the solution on a part of the boundary allows us to get back a weakened energy of the initial data, this if the coupling parameter is sufficiently small, but non vanishing. This result leads to a new uniqueness theorem and also to an indirect exact controllability result.