Dynamic transmission conditions for linear hyperbolic systems on networks

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 eithe...

Ausführliche Beschreibung

Gespeichert in:

Bibliographische Detailangaben
Veröffentlicht in:	Journal of evolution equations 2021-09, Vol.21 (3), p.3639-3673
Hauptverfasser:	Kramar Fijavž, Marjeta, Mugnolo, Delio, Nicaise, Serge
Format:	Artikel
Sprache:	eng
Schlagworte:	Analysis Analysis of PDEs Hyperbolic systems Linear algebra Mathematics Mathematics and Statistics Networks
Online-Zugang:	Volltext
Tags:	Tag hinzufügen Keine Tags, Fügen Sie den ersten Tag hinzu!

Beschreibung
Zusammenfassung:	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.
ISSN:	1424-3199 1424-3202
DOI:	10.1007/s00028-021-00715-0