Asymptotic property of a reparable multi-state device

Abstract

This paper is devoted to studying the existence, uniqueness and asymptotic stability of a multi-state device’s time-dependent solution. C 0 C_0 semigroup theory is used to prove the existence of a unique non-negative solution of the device. Moveover, by analyzing the spectrum of the system operator generated by the device, this paper proves that 0 is the unique spectral point on the imaginary axis and the other spectra lie in the left half plane. As a result, the asymptotic behavior of a multi-state device is obtained.