Stability analysis of the telegrapher's equations with dynamic boundary condition

This paper is concerned with the stability analysis of a distributed parameter circuit with dynamic boundary condition. The distributed parameter circuit is written by the telegrapher's equations whose boundary condition is described by an ordinary differential equation. First of all, it is shown that, for any physical parameters of the circuit, the system operator generates an exponentially stableC0-semigroup on a Hilbert space. However, it is not clear whether the decay rate of the semigroup is the most precise one. In this paper, the spectral analysis is conducted for the system satisfying the distortionless condition, and it is shown that the semigroup satisfies the spectrum determined growthcondition.