Semigroups for dynamical processes on metric graphs

Kramar Fijavž, Marjeta (author), Puchalska, Aleksandra (author)

We present the operator semigroups approach to the first- and second-order dynamical systems taking place on metric graphs. We briefly survey the existing results and focus on the well-posedness of the problems with standard vertex conditions. Finally, we show two applications to biological models. This article is part of the theme issue "Semigroup applications everywhere".

• Language: English
• Keywords: analysis, differential equations, biomathematics, operator semigroups, networks, transport equation, diffusion equation, genetic mutation model, synaptic transmission model
• 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: 2020
• Number of pages: Str. 1-17
• Numbering: Vol. 378, no. 2158
• PID: 20.500.12556/RUL-125093
• UDC: 51
• ISSN on article: 1364-503X
• DOI: 10.1098/rsta.2019.0619
• COBISS.SI-ID: 37675779
• Publication date in RUL: 04.03.2021

Record is a part of a journal

• Title: Philosophical transactions
• Shortened title: Philos. trans. - Royal Soc., Math. phys. eng. sci.
• Publisher: Royal Society
• ISSN: 1364-503X
• COBISS.SI-ID: 17265413

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.
• Licensing start date: 04.03.2021

Secondary language

• Language: Slovenian
• Title: Polgrupe za dinamične procese na metričnih grafih

Abstract

Predstavimo operatorsko polgrupni pristop k dinamičnim sistemom prvega in drugega reda na metričnih grafih. Na kratko strnemo obstoječe rezultate in se osredotočimo na dobro pogojenost problema s standardnimi pogoji v vozliščih. Na koncu prikažemo dve uporabi na modelih v biologiji. Članek je del vsebinske izdaje "Semigroup applications everywhere".

• Keywords: akademska matematika, operatorske polgrupe, omrežja, transportna enačba

Projects

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

• Funder: EC - European Commission
• Project number: CA18232