Study On The Dynamic Solution Of A Deteriorating System With Delayed Vacation Of A Repairman

In this paper,we use C₀-semigroup theory and operator theory to study the well posedness of a deteriorating system with delayed vacation of a repairman,which is de-scribed by infinitely many partial differential equations.First,we rewrite the mathemat-ical model of a deteriorating system with delayed vacation of a repairman as an abstract Cauchy problem in a suitable Banach space;Next,we give the explicit form of the Dirichlet operator and characteristic equations,which correspond to the system operator;Finally,we show that the system operator generates a positive contraction C₀-semigroup,so as to get the conclusion that the system is well posed and the nonnegative dynamic solution of the system exist and be unique.