Dynamic transmission conditions for linear hyperbolic systems on networks

Kramar Fijavž, Marjeta (author), Mugnolo, Delio (author), Nicaise, Serge (author)

We study evolution equations on networks that can be modeled by means of hyperbolic systems. We extend our previous findings in Kramar et al. (Linear hyperbolic systems on networks. arXiv:2003.08281, 2020) by discussing well-posedness under rather general transmission conditions that might be either of stationary or dynamic type—or a combination of both. Our results rely upon semigroup theory and elementary linear algebra. We also discuss qualitative properties of solutions.

• Language: English
• Keywords: mathematics, hyperbolic systems, operator semigroups, dynamic boundary conditions, PDEs on networks, invariance properties, second sound
• 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: 2021
• Number of pages: Str. 3639-3673
• Numbering: Vol. 21, iss. sept.
• PID: 20.500.12556/RUL-133733
• UDC: 517.956.3
• ISSN on article: 1424-3199
• DOI: 10.1007/s00028-021-00715-0
• COBISS.SI-ID: 88859395
• Publication date in RUL: 13.12.2021

Record is a part of a journal

• Title: Journal of evolution equations
• Shortened title: J. evol. equ.
• Publisher: Birkhäuser
• ISSN: 1424-3199
• COBISS.SI-ID: 514904345

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.
• Licensing start date: 27.05.2021

Secondary language

• Language: Slovenian
• Keywords: matematika, hiperbolični sistemi, operatorske polgrupe, dinamični robni pogoji, PDE na omrežjih, invariantne lastnosti, drugi zvok