Open AccessBi-Continuous semigroups for flows on infinite networks
Author(s) -
Christian Budde,
Marjeta Kramar Fijavž
Publication year - 2021
Publication title -
networks and heterogeneous media
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.732
H-Index - 34
eISSN - 1556-181X
pISSN - 1556-1801
DOI - 10.3934/nhm.2021017
Subject(s) - mathematics , boundary (topology) , operator (biology) , semigroup , matrix (chemical analysis) , metric (unit) , constant (computer programming) , hölder condition , combinatorics , discrete mathematics , pure mathematics , mathematical analysis , computer science , biochemistry , chemistry , materials science , operations management , repressor , transcription factor , economics , composite material , gene , programming language
We study transport processes on infinite metric graphs with non-constant velocities and matrix boundary conditions in the \begin{document}$ {\mathrm{L}}^{\infty} $\end{document} -setting. We apply the theory of bi-continuous operator semigroups to obtain well-posedness of the problem under different assumptions on the velocities and for general stochastic matrices appearing in the boundary conditions.