Analysis Of The Solution Of A Parallel Maintenance System With Two Component

This paper studied The property of two components in parallel maintenance system operator, by transfering the model into Volterra equation of Banach space. Firstly, systems exist only non-negative strong solution is proved, and the Co semigroup theory is used to prove system operator is a type of the thick set resolvent positive operator, the adjoint operator of the system operator is obtained and its domain. Zero is eigenvalue of system operator whose geometric multiplicity is one, Zero is eigenvalue of conjugate operator whose geometric multiplicity is one, feature vector (1,1,1,1,1)T is zero, and zero is eigenvalue of system operator whose algebric multiplicity is one. Secondly, the preliminary solution is operator tail concepts and related theories is used to prove system exists only non-negative weak solution. Finally, by analysis of spectral distribution system operator and the nature of the system operator, find out the spectral point of system operator are located in the left half plane of complex plane,except zero point have no spectral point on imaginary axis,and the system is asymptotically stable.