{"title":"具有延迟边界条件的波动方程的稳定性分析","authors":"Li Zhang , Gabor Stepan","doi":"10.1016/j.piutam.2017.08.018","DOIUrl":null,"url":null,"abstract":"<div><p>Stability of the 1D wave equation with delayed boundary conditions is considered. By means of the traveling wave solution, the original system is transformed into a delay differential equation of neutral type which involves two delays. The complete and exact stability chart is presented for the delayed boundary problem in the parameter plane of the feedback gain between the boundaries and the ratio of the time delays.</p></div>","PeriodicalId":74499,"journal":{"name":"Procedia IUTAM","volume":"22 ","pages":"Pages 139-145"},"PeriodicalIF":0.0000,"publicationDate":"2017-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.piutam.2017.08.018","citationCount":"2","resultStr":"{\"title\":\"Stability Analysis of the Wave Equation with Delayed Boundary Conditions\",\"authors\":\"Li Zhang , Gabor Stepan\",\"doi\":\"10.1016/j.piutam.2017.08.018\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>Stability of the 1D wave equation with delayed boundary conditions is considered. By means of the traveling wave solution, the original system is transformed into a delay differential equation of neutral type which involves two delays. The complete and exact stability chart is presented for the delayed boundary problem in the parameter plane of the feedback gain between the boundaries and the ratio of the time delays.</p></div>\",\"PeriodicalId\":74499,\"journal\":{\"name\":\"Procedia IUTAM\",\"volume\":\"22 \",\"pages\":\"Pages 139-145\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2017-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1016/j.piutam.2017.08.018\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Procedia IUTAM\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S2210983817301074\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Procedia IUTAM","FirstCategoryId":"1085","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S2210983817301074","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Stability Analysis of the Wave Equation with Delayed Boundary Conditions
Stability of the 1D wave equation with delayed boundary conditions is considered. By means of the traveling wave solution, the original system is transformed into a delay differential equation of neutral type which involves two delays. The complete and exact stability chart is presented for the delayed boundary problem in the parameter plane of the feedback gain between the boundaries and the ratio of the time delays.
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