Explicit formulae for limit periodic flows on networks

dc.contributor.authorBanasiak, Jacek
dc.contributor.emailjacek.banasiak@up.ac.zaen_ZA
dc.date.accessioned2016-06-23T07:06:32Z
dc.date.issued2016-07
dc.description.abstractIn recent papers it was shown that, under certain conditions, the C0-semigroup describing a flow on a network (metric graph) that contains terminal strong (ergodic) components converges to the direct sum of periodic semigroups generated by the flows on these components. In this note we shall provide an explicit description of these limit semigroups in terms of the components of the adjacency matrix of the line graph of the network. The result is based on the Frobenius–Perron theory and the estimates of long term behaviour of iterates of reducible matrices.en_ZA
dc.description.departmentMathematics and Applied Mathematicsen_ZA
dc.description.embargo2017-06-30
dc.description.librarianhb2016en_ZA
dc.description.sponsorshipNational Research Foundation of South Africa, Grant No: 102275.en_ZA
dc.description.urihttp://www.elsevier.com/locate/laaen_ZA
dc.identifier.citationBanasiak, J 2016, 'Explicit formulae for limit periodic flows on networks', Linear Algebra and Its Applications, vol. 500, pp. 30-42en_ZA
dc.identifier.issn0024-3795
dc.identifier.other10.1016/j.laa.2016.03.010
dc.identifier.urihttp://hdl.handle.net/2263/53370
dc.language.isoenen_ZA
dc.publisherElsevieren_ZA
dc.rights© 2016 Elsevier Inc. All rights reserved. Notice : this is the author’s version of a work that was accepted for publication in Linear Algebra and Its Applications. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Linear Algebra and Its Applications, vol. 500, pp. 30-45, 2016. doi : 10.1016/j.laa.2016.03.010.en_ZA
dc.subjectTransport on networksen_ZA
dc.subjectPerron–Frobenius theoryen_ZA
dc.subjectDigraphsen_ZA
dc.subjectLine graphsen_ZA
dc.subjectReducible matricesen_ZA
dc.subjectImprimitive matricesen_ZA
dc.subjectC0-semigroupsen_ZA
dc.titleExplicit formulae for limit periodic flows on networksen_ZA
dc.typePostprint Articleen_ZA

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