{"title":"Well-posedness of flows in networks with output","authors":"F. Zheng","doi":"10.1109/ISKE.2010.5680803","DOIUrl":null,"url":null,"abstract":"In this note, the transport processes in networks with space dependent velocities on edges and output in a node was discussed by combining functional analytical and graph theoretical methods. This problem was converted into the terminology of operator semigroups and an abstract Cauchy problem was obtained on a suitable Banach space. The well-posedness of the system was given by showing the system operator generates a c0 semigroups.","PeriodicalId":6417,"journal":{"name":"2010 IEEE International Conference on Intelligent Systems and Knowledge Engineering","volume":"122 1","pages":"98-101"},"PeriodicalIF":0.0000,"publicationDate":"2010-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"2010 IEEE International Conference on Intelligent Systems and Knowledge Engineering","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/ISKE.2010.5680803","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
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Abstract
In this note, the transport processes in networks with space dependent velocities on edges and output in a node was discussed by combining functional analytical and graph theoretical methods. This problem was converted into the terminology of operator semigroups and an abstract Cauchy problem was obtained on a suitable Banach space. The well-posedness of the system was given by showing the system operator generates a c0 semigroups.
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