{"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":null,"pages":null},"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}
引用次数: 2
Abstract
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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