Dynamic Transmission Conditions for Linear Hyperbolic Systems on Networks
Marjeta Kramar Fijav\v{z}, Delio Mugnolo, Serge Nicaise
TL;DR
This paper investigates well-posedness and qualitative properties of hyperbolic systems on networks with general stationary and dynamic transmission conditions, extending previous work using semigroup theory and linear algebra.
Contribution
It introduces a comprehensive framework for analyzing hyperbolic systems on networks with mixed transmission conditions, broadening the scope of prior results.
Findings
Established well-posedness under general transmission conditions
Analyzed qualitative properties of solutions
Extended previous results to dynamic and combined conditions
Abstract
We study evolution equations on networks that can be modeled by means of hyperbolic systems. We extend our previous findings in \cite{KraMugNic20} 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.
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