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arXiv · 2503.08809

Abstract boundary delay systems and application to network flow

András Bátkai·Marjeta Kramar Fijavž·Abdelaziz Rhandi
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Abstract

This paper investigates the well-posedness and positivity of solutions to a class of delayed transport equations on a network. The material flow is delayed at the vertices and along the edges. The problem is reformulated as an abstract boundary delay equation, and well-posedness is proved by using the Staffans-Weiss theory. We also establish spectral theory for the associated delay operators and provide conditions for the positivity of the semigroup.

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András Bátkai, Marjeta Kramar Fijavž, Abdelaziz Rhandi. 2025-03-11. Abstract boundary delay systems and application to network flow. https://doi.org/10.1002/mma.70139

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