Asymptotic periodicity of flows in time-depending networks

TL;DR

This paper studies the long-term behavior of solutions to a linear transport equation on networks with time-dependent coefficients, establishing well-posedness and asymptotic periodicity, with applications to air traffic management.

Contribution

It introduces a framework for analyzing asymptotic periodicity in time-varying network flows using non-autonomous Cauchy problem methods, extending existing theories.

Findings

Proved well-posedness of the transport equation on time-dependent networks.

Characterized the asymptotic profile of solutions under natural conditions.

Applied the theory to an air traffic flow management model.

Abstract

We consider a linear transport equation on the edges of a network with time-varying coefficients. Using methods for non-autonomous abstract Cauchy problems, we obtain well-posedness of the problem and describe the asymptotic profile of the solutions under certain natural conditions on the network. We further apply our theory to a model used for air traffic flow management.