Abstract boundary delay systems and application to network flow
Analysis of PDEs
2025-11-11 v2 Functional Analysis
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.
Cite
@article{arxiv.2503.08809,
title = {Abstract boundary delay systems and application to network flow},
author = {András Bátkai and Marjeta Kramar Fijavž and Abdelaziz Rhandi},
journal= {arXiv preprint arXiv:2503.08809},
year = {2025}
}
Comments
20 pages