{"title":"电报系统的网络和港口汉密尔顿。Ⅲ。显性表征和长期行为","authors":"J. Banasiak, Adam Bloch","doi":"10.3934/eect.2022016","DOIUrl":null,"url":null,"abstract":"In this paper we present an explicit formula for the semigroup governing the solution to hyperbolic systems on a metric graph, satisfying general linear Kirchhoff's type boundary conditions. Further, we use this representation to establish the long term behaviour of the solutions. The crucial role is played by the spectral decomposition of the boundary matrix.","PeriodicalId":176362,"journal":{"name":"Evolution Equations & Control Theory","volume":"173 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2021-11-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Telegraph systems on networks and port-Hamiltonians. Ⅲ. Explicit representation and long-term behaviour\",\"authors\":\"J. Banasiak, Adam Bloch\",\"doi\":\"10.3934/eect.2022016\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper we present an explicit formula for the semigroup governing the solution to hyperbolic systems on a metric graph, satisfying general linear Kirchhoff's type boundary conditions. Further, we use this representation to establish the long term behaviour of the solutions. The crucial role is played by the spectral decomposition of the boundary matrix.\",\"PeriodicalId\":176362,\"journal\":{\"name\":\"Evolution Equations & Control Theory\",\"volume\":\"173 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2021-11-16\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Evolution Equations & Control Theory\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.3934/eect.2022016\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Evolution Equations & Control Theory","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.3934/eect.2022016","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Telegraph systems on networks and port-Hamiltonians. Ⅲ. Explicit representation and long-term behaviour
In this paper we present an explicit formula for the semigroup governing the solution to hyperbolic systems on a metric graph, satisfying general linear Kirchhoff's type boundary conditions. Further, we use this representation to establish the long term behaviour of the solutions. The crucial role is played by the spectral decomposition of the boundary matrix.