Flows on metric graphs with general boundary conditions
type: Item
instance of: scholarly article
title: Flows on metric graphs with general boundary conditions
published in: Journal of Mathematical Analysis and Applications
publication date: 2022-05-03T00:00:00Z
full work available at URL: https://arxiv.org/abs/2110.08553
review text: In this article the authors study the generation of \(\text{C}_0\)-semigroups by first order differential operators on \(\operatorname{L}^p(\mathbb{R}_+,\mathbb{C}^\ell)\times\operatorname{L}^p([0,1],\mathbb{C}^m)\) with general boundary conditions. The authors first characterize the generation property in terms of the invertibility of a matrix associated to the boundary conditions under certain technical conditions on the coefficients of the differential operator. Then they employ their abstract results to study well-posedness of transport equations on non-compact metric graphs. This includes in particular graphs with infinitely many edges or with edges that represent semi-axes.
reviewed by: Sven-Ake Wegner
Mathematics Subject Classification ID: 47D03
Mathematics Subject Classification ID: 34G10
Mathematics Subject Classification ID: 47D06
zbMATH DE Number: 7516724
zbMATH Keywords: first order differential operators
zbMATH Keywords: transport equation
zbMATH Keywords: \(C_0\)-semigroups
zbMATH Keywords: flows on networks
zbMATH Keywords: non-compact metric graphs
author: Klaus-Jochen Engel
author: Marjeta Kramar Fijavž
MaRDI profile type: Publication
OpenAlex ID: W3205817246
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DOI: 10.1016/J.JMAA.2022.126214
description: scientific article; zbMATH DE number 7516724