Abstract Boundary Delay Systems and Application to Network Flow

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.