Asymptotic Property of the Solution of the Reliability Model for the Supply Chain

We study asymptotic property of the solution of the reliability model for the supply chain by using C0-semigroup theory.Firstly we prove that all points on the imaginary axis except for zero belong to the resolvent set of the operator corresponding to the model.Secondly we prove that 0 is an eigenvalue of the operator and its adjoint operator with geometric multiplicity and algebraic multiplicity.By using the above results we obtain that the time-dependent solution of the model strongly converges to the steady-state solution of the model.