Flows on metric graphs with general boundary conditions

Engel, Klaus-Jochen (author), Kramar Fijavž, Marjeta (author)

In this note we study the generation of C$_0$-semigroups by first-order differential operators on L$^p(\mathbb{R}_+, \mathbb{C}^l$) × L$^p$([0, 1], $\mathbb{C}^m$) with general boundary conditions. In many cases we are able to characterize the generation property in terms of the invertibility of a matrix associated to the boundary conditions. The abstract results are used to study the well-posedness of transport equations on non-compact metric graphs.

• Language: English
• Keywords: first order differential operators, transport equation, C$_0$-semigroups, flows on networks, non-compact metric graphs
• 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: 2022
• Number of pages: 27 str.
• Numbering: Vol. 513, iss. 2, art. 126214
• PID: 20.500.12556/RUL-136221
• UDC: 517.98
• ISSN on article: 0022-247X
• DOI: 10.1016/j.jmaa.2022.126214
• COBISS.SI-ID: 105351427
• Publication date in RUL: 20.04.2022

Record is a part of a journal

• Title: Journal of mathematical analysis and applications
• Shortened title: J. math. anal. appl.
• Publisher: Elsevier
• ISSN: 0022-247X
• COBISS.SI-ID: 3081231

Licences

• License: CC BY-NC-ND 4.0, Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International
• Link: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Description: The most restrictive Creative Commons license. This only allows people to download and share the work for no commercial gain and for no other purposes.

Secondary language

• Language: Slovenian
• Keywords: diferencialni operatorji prvega reda, transportna enačba, C$_0$-polgrupe, pretoki v omrežjih, nekompaktni metrični grafi

Projects

• Funder: Other - Other funder or multiple funders
• Funding programme: COST
• Project number: CA18232

• Funder: ARRS - Slovenian Research Agency
• Project number: P1-0222
• Name: Algebra v teoriji operatorjev in finančna matematika