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The main result of the paper is then to supplement these previous results by showing how a new Lyapunov stability approach can be used for the analysis of boundary conditions that are known to be dissipative for the $C^1$-norm.<\/jats:p>","DOI":"10.1137\/14097080x","type":"journal-article","created":{"date-parts":[[2015,6,9]],"date-time":"2015-06-09T11:43:50Z","timestamp":1433850230000},"page":"1464-1483","source":"Crossref","is-referenced-by-count":52,"title":["Dissipative Boundary Conditions for One-Dimensional Quasi-linear Hyperbolic Systems: Lyapunov Stability for the $C^1$-Norm"],"prefix":"10.1137","volume":"53","author":[{"given":"Jean-Michel","family":"Coron","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Georges","family":"Bastin","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2015,6,9]]},"reference":[{"key":"atypb1","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.2012.2228035"},{"key":"atypb2","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.2011.2158171"},{"key":"atypb3","doi-asserted-by":"publisher","DOI":"10.1016\/j.sysconle.2011.07.008"},{"key":"atypb4","unstructured":"G. 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