Abstract boundary delay systems and application to network flow

Bátkai, András (author), Kramar Fijavž, Marjeta (author), Rhandi, Abdelaziz (author)

This paper investigates the well-posedness and positivity of solutions to a class of delayed transport equations on a network. The material flow is delayed at the vertices and along the edges. The problem is reformulated as an abstract boundary delay equation, and well-posedness is proved by using the Staffans–Weiss theory. We also establish spectral theory for the associated delay operators and provide conditions for the positivity of the semigroup.

• Language: English
• Keywords: metric graph, network flow, operator semigroup, perturbation of a generator, transport equation with delay, well-posed linear system
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: FGG - Faculty of Civil and Geodetic Engineering
• Publication status: Published
• Publication version: Version of Record
• Year: 2026
• Number of pages: Str. 119-129
• Numbering: Vol. 49, iss. 1
• PID: 20.500.12556/RUL-175301
• UDC: 519.17
• ISSN on article: 0170-4214
• DOI: 10.1002/mma.70139
• COBISS.SI-ID: 254414851
• Publication date in RUL: 15.12.2025

Record is a part of a journal

• Title: Mathematical methods in the applied sciences
• Shortened title: Math. methods appl. sci.
• Publisher: Wiley
• ISSN: 0170-4214
• COBISS.SI-ID: 25911808

Licences

• License: CC BY 4.0, Creative Commons Attribution 4.0 International
• Link: http://creativecommons.org/licenses/by/4.0/
• Description: This is the standard Creative Commons license that gives others maximum freedom to do what they want with the work as long as they credit the author.

Secondary language

• Language: Slovenian
• Keywords: metrični grafi, pretok v omrežju, operatorske polgrupe, sprememba generatorja, transportna enačba z zakasnitvijo, dobro zastavljeni linearni sistemi