Analysis of coupled Maxwell-cable problems

TL;DR

This paper analyzes the mathematical properties of a coupled Maxwell-cable model, establishing conditions for well-posedness and the generation of a strongly continuous semigroup, thereby advancing understanding of electromagnetic-cable interactions.

Contribution

It provides a rigorous analysis of the qualitative properties of the coupled Maxwell-cable system, including well-posedness and semigroup generation, building on previous modeling work.

Findings

The autonomous system generates a strongly continuous semigroup.

Sufficient conditions for well-posedness are established.

The model ensures continuous dependence on inputs and initial conditions.

Abstract

Building on the recently published work "Modeling of radiating curved cables via coupled telegrapher's and Maxwell's equations", which introduces a model for the interaction between electromagnetic fields and radiating (possibly curved) cables, we analyze the qualitative properties of the resulting dynamical system. The model features inputs and outputs given by the currents and voltages at the cable ends, while the state comprises the corresponding distributions along the cables and the electromagnetic fields in the surrounding domain. We show that the autonomous dynamics (i.e., with zero input) generate a strongly continuous semigroup and establish sufficient conditions for well-posedness, meaning continuous dependence of the state and output trajectories on the inputs and initial conditions.