Perturbations of finite networks and asymptotic periodicity of flow semigroups
type: Item
instance of: scholarly article
title: Perturbations of finite networks and asymptotic periodicity of flow semigroups
zbMATH Open document ID: 1177.47050
author: Dávid Kunszenti-Kovács
published in: Semigroup Forum
publication date: 2009-10-14T00:00:00Z
review text: The asymptotic behaviour of transport flows in networks and related questions have lately been treated in several articles, extending the original problem from finite to infinite networks and studying several different types of convergence of the corresponding semigroup flow. The goal of this article is a new, less abstract approach to the problem allowing better understanding of the underlying mechanism of flow in networks. The relevance of cycle lengths rather than edge lengths in connection with asymptotic behaviour is examined in Section~3, through a perturbation method applied to the network itself. The perturbation method is presented in the setting of finite strongly connected network. In the author's paper [``Perturbations of networks and asymptotic periodicity of recurrent flows: the infinite case'' (Preprint, 2008)], this technique is adapted to infinite networks, where it allows for significant generalizations of previous results. Also, the author indicates some connections between flows in networks and Markov chains.
reviewed by: V. Lokesha
Mathematics Subject Classification ID: 47D03
Mathematics Subject Classification ID: 90B10
Mathematics Subject Classification ID: 05C99
Mathematics Subject Classification ID: 82C70
zbMATH DE Number: 5614938
zbMATH Keywords: flow semigroup
zbMATH Keywords: transport equation
zbMATH Keywords: asymptotic behaviour
zbMATH Keywords: network perturbation
zbMATH Keywords: factor network
MaRDI profile type: Publication
full work available at URL: s00233-008-9131-z
OpenAlex ID: W2082722875
cites work: Q4398864
cites work: Semigroups for flows in infinite networks
cites work: Asymptotic periodicity of recurrent flows in infinite networks
cites work: One-Parameter Semigroups for Linear Evolution Equations
cites work: Q4094202
cites work: Network Perturbations and Asymptotic Periodicity of Recurrent Flows in Infinite Networks
cites work: Spectral properties and asymptotic periodicity of flows in networks
cites work: Asymptotic behavior of flows in networks
DOI: 10.1007/S00233-008-9131-Z
description: scientific article; zbMATH DE number 5614938